problem solving unitary method

Unitary Method

Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit. It is a method that we use for most of the calculations in math. You will find this method useful while solving questions on ratio and proportion , algebra , geometry, etc.

Through the unitary method, we can find the missing value. For example, if 1 packet of juice costs $5, then what would the cost of 5 such packets be? Then we can easily find that the cost of 5 packets, i.e. $25. Let's understand this concept in detail in this lesson.

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What is Unitary Method?

Let's recap the unitary method definition. "It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit."

Here is a situation to understand this method. Emma went to an ice cream parlor and bought 5 ice-creams. She paid $125 to the shopkeeper. The next day, she again goes to the same parlor and orders 3 icecreams. So, how much will she be paying for 3 ice-creams? This may seem hard to calculate! However, we can solve this problem using the unitary method.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

In the unitary method, the value of many things is given and we need to either find the value of more or fewer things. In order to do that, we must first find the value of one thing by division and then find the value of more or fewer things by multiplication .

Types of Unitary Method

In the unitary method, we always count the value of a unit or one quantity first, and then we calculate the values of more or fewer quantities. That is why this method is termed the unitary method. There are two types of unitary methods because they result in two types of variations and those are given below:

Direct Variation
Indirect Variation

Direct Variation in Unitary Method

This type describes the direct relationship between two quantities. In simple words, if one quantity increases, the other quantity also increases, and if one quantity decreases, the other quantity also decreases. For example, If the speed of a car is increased, it covers more distance in a fixed amount of time. So, speed and distance are two quantities that are related to each other in direct variation.

Indirect Variation in Unitary Method

This type describes the indirect relationship between two quantities. In simple words, if one quantity increases, the other quantity decreases, and if one quantity decreases the other quantity increases. For example, increasing the speed of the car will result in covering a fixed distance in lesser time. Speed and time are two quantities that are related to each other in indirect variation.

Unitary Method in Ratio and Proportion

Unitary method in maths is also used to find the ratio between two quantities. Consider the following situation. A contractor employed two men, Ryan and David, to work in his factory and paid them daily wages. Ryan is paid $150 and David is paid $110 for each day's work. Ryan saves $800 per month and David saves $500 per month. Can you find the ratio of their monthly expenditure?

Let’s find their monthly income by using the unitary method. Ryan’s wages for one day= $150. Ryan’s wages for one month= $(150 × 30) = $4500. Similarly, David’s wages for one month= $(110 × 30) = $3300.
Now find their monthly expenditure. Ryan’s monthly expenditure = $4500 - $800 = $3700. David’s monthly expenditure = $3300 - $500 = $2800.
The ratio of their monthly expenditure is given by, Ryan’s monthly expenditure/David’s monthly expenditure=3700/2800=37/28.

Proportion is defined as the relationship between two ratios. So, with the help of the unitary method, we can also find the missing value in the given proportion of two quantities. For example, if the cost and number of balloons sold by two different sellers are defined in a proportion as 3:4::15:x. Here we can find the missing value of x by using the concept of the unitary method. If the cost of 4 balloons is $3, then the number of balloons bought in $15 is 3/4 = 15/x, which is the same as, 3x=60. So, the number of balloons is 20.

Let's move on to solve some more real-life problems based on the unitary method.

Real-Life Applications of Unitary Method

Unitary method is very helpful in solving various problems that we come across in our daily life. Some of those real-life applications of the unitary method are given below:

To find the speed of an object for a given distance, if the speed and distance are given in different quantities.
To find the number of people required to complete a given amount of work.
To find the area of a square of a given length if the ratio of its area and side is given.
To find the cost of a specific number of objects, if the cost and number of objects are given in different quantities.
To find the percentage of a quantity.

Important Notes:

The value of many quantities is found by multiplying the value of one quantity by the number of quantities.
The value of one quantity is found by dividing the value of many quantities by the number of quantities.

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Unitary Method Word Problems

Example 1: Ron goes to a stationery shop to buy some notebooks. The shopkeeper informs him that 2 notebooks would cost $90. Can you find the cost of 5 notebooks with the help of the unitary method?

In this example, the number of books corresponds to the “unit” and the cost of the books corresponds to the “value”. Let's solve it step-wise.

Step 1: First, we will find the cost of 1 notebook. Cost of 1 notebook= Total cost of books/Total number of books= 90/2= $45.
Step 2: Now, we will find the cost of 5 notebooks. Cost of 5 notebooks= Cost of 1 book × Number of books= 45 × 5= 225.

Therefore, the cost of 5 notebooks is $225.

Example 2: Rachel can type 540 words in half an hour. How many words will she be able to type in 20 minutes with the same efficiency?

The number of words typed in half an hour i.e. 30 min = 540. Therefore, by using the unitary method we can find the number of words typed in a minute. Number of words typed in 1 min = 540/30=18.

Number of words typed in 20 min = 20 × 18 = 360.

Hence, Rachel will be able to type 360 words in 20 minutes.

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Practice Questions on Unitary Method

Faqs on unitary method, how do you solve unitary method questions.

To solve questions based on the unitary method, we have to first find the number of objects at the unit level, then we find it for higher values. For example, if the cost of 5 chocolates is $10, then to find the cost of 6 chocolates, it is better to find the cost of 1 chocolate first. Then we multiply it by 6 to get the cost of 6 chocolates.

What is the Unitary Method for Percentage?

To find the 100 th amount or the value of an object, the unitary method is used. Consider the following example. In a hospital, 10% of the monthly consumption of milk of patients is 1540L. What is the 100% monthly consumption of milk in the hospital? In this case, the unitary method can be used to find the 1% monthly consumption and then multiply 100 by the amount of 1% of monthly consumption of milk.

What is the Formula for Unitary Method?

The formula for the unitary method is to find the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

What is the Unitary Ratio?

When either side of the ratio is equal to 1 it is called unitary ratio. The unitary method in maths uses this for comparison. For example, there are 10 girls and 20 boys in a class. The ratio of girls to boys is 1:2. This is a unitary ratio.

What are the Types of Unitary Method?

There are two types of unitary methods based on the variations and those are given below:

What is Unitary Method in Ratio and Proportion?

In ratio and proportion, the unitary method is used to find the quantity of one object when the quantity of another object and the ratio between two are given.

Mastering Math Made Easy: How to Use the Unitary Method

Author: Noreen Niazi
Last Updated on: August 22, 2023

$Unitary method$

Math can be difficult for many people, but it doesn’t have to be. One of the keys to mastering math is to learn how to use various problem-solving methods. One such method is the Unitary Method. This article will provide an in-depth guide to understanding and using the Unitary Method and tips for applying it to various math concepts.

Introduction

The Unitary Method is a problem-solving technique commonly used in math. It involves using the relationships between different units of measurement to solve problems. For example, if you know that 1 meter equals 100 centimeters, you can use this relationship to convert between the two units. This is a simple example of the Method in action.

One of the benefits of this method is that it can be used to solve a wide variety of problems. It can be applied to problems involving distance, weight, time, money, and more. Additionally, it is a flexible method that can be combined with other problem-solving techniques.

Understanding the Method: Definition and Examples

Defining and providing some examples is important to fully understand the Unitary Method. This Method involves finding a relationship between two units of measurement and using that relationship to solve a problem. For example, if you know that 1 kilogram equals 1000 grams, you can use this relationship to convert between the two units.

Another example of the Method in action is solving a problem involving time. If 1 hour equals 60 minutes, you can use this relationship to convert between the two units. For example, if you need to convert 2 hours to minutes, you would multiply 2 by 60 to get 120 minutes.

Applications in Real-Life Situations

$Unitary method, mass unit conversion$

The Unitary Method has many practical applications in real-life situations. For example, it can be used in cooking to convert between different units of measurement. If a recipe calls for 1 tablespoon of sugar and you only have a measuring cup, you can use this method to convert between the two units.

This method can also be used in finance to calculate interest rates. For example, if you know that the interest rate on a loan is 5% per year, you can use the Unitary Method to calculate the interest for a specific period. Additionally, this method can be used in construction to calculate the material needed for a project.

Advantages of Using the Unitary Method in Math Problem Solving

There are several advantages to using the Unitary Method in math problem-solving . One of the main advantages is that it is a flexible method that can be used to solve various problems. Additionally, it is a simple and easy-to-understand method that people of all ages and skill levels can use.

Another advantage of the Unitary Method is that it is a visual method that can help students understand the relationships between different units of measurement. This can help them better understand math concepts and improve their problem-solving skills.

Step-by-Step Guide to Using the Unitary Method

$money conversion by Unitary method$

To use the Unitary Method, follow these steps:

Identify the two units of measurement involved in the problem.
Determine the relationship between the two units of measurement.
Use the relationship to convert between the two units of measurement.
Solve the problem using the converted units of measurement.

For example, if you need to convert 2 meters to centimeters, you would follow these steps:

Identify the two units of measurement: meters and centimeters.
Determine the relationship between the two units: 1 meter equals 100 centimeters.
Use the relationship to convert 2 meters to centimeters: 2 meters x 100 centimeters/meter = 200 centimeters.
Solve the problem using the converted units of measurement: 2 meters is equal to 200 centimeters.

Common Mistakes to Avoid

While the Unitary Method is a simple and effective problem-solving technique, people make common mistakes. One of the most common mistakes is forgetting to convert the measurement units correctly. This can lead to incorrect answers and confusion.

Another common mistake is using the wrong relationship between units of measurement. For example, if you need to convert meters to centimeters, you would use the relationship 1 meter = 100 centimeters. Using the wrong relationship, such as 1 meter = 10 centimeters, can lead to incorrect answers.

Practice Problems

To master the method, it is important to practice solving problems using the technique. Here are some practice problems to help you get started:

Convert 3 kilometers to meters.
Convert 4 hours to minutes.
Convert 500 milliliters to liters.
Calculate the interest on a loan with a principal of $1000 and an interest rate of 6% per year for 2 years.
Determine the amount of paint needed to paint a room 10 meters long, 5 meters wide, and 3 meters high.

Additional Resources for Learning and Practicing the Method

Many resources are available to learn more about the Unitary Method or practice using the technique. Online math websites like Khan Academy offer tutorials and practice problems. Additionally, many math textbooks and workbooks cover this Method in depth.

Tips for Applying the Method in Various Math Concepts

The Unitary Method can be applied to various math concepts, including fractions, ratios, and percentages. When applying the Method to these concepts, it is important to understand the relationship between the units of measurement involved. For example, using the Unitary Method when working with fractions, you may need to convert between different denominators.

The Unitary Method is a powerful problem-solving technique that can be used to solve various math problems. It is a flexible and easy-to-understand method used by people of all ages and skill levels. Following the steps outlined in this article and practicing with the provided problems, you can master the Unitary Method and improve your math skills.

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Unitary Method

In our daily lives when buying items like vegetables, the seller mentions the wholesale prices. For example, suppose we buy 5kg of sugar for 100 Rs. How can we find out the price for a unit kg that is 1 kg of sugar? The answer to this is the unitary method. Further, we can use this to calculate the price of multiple units, given the knowledge of the cost of a single unit. Given its importance in our daily lives, let us understand about the unitary method.

Browse more Topics under Ratios And Proportions

Introduction to Ratio and Proportion

Understand the concept of Ratio and Proportion in detail here .

Solved Examples for You

Question 1: The cost of 10 notebooks is 300 Rs. Find:

The number of notebooks that can be purchased with 420 Rs.
The cost of 5 notebooks

Answer : It is given that the cost of 10 notebooks = 300 Rs. Hence the cost of 1 notebook = 30 Rs. Now,

The number of notebooks that can be purchased with 30 Rs. = 1. The number of notebooks that can be purchased with 1 Re. = 1/30. Hence, the number of notebooks that can be purchased with 420 Rs. = 1/30 ×420= 14 notebooks
The cost of 1 notebook = 30 Rs. The cost of 5 notebooks = 30 Rs. × 5 = 150 Rs.

Question 2: If 45 students can consume a stock of food in 22 months, then for how many days the same stock of food will last for 27 students?

Answer : The correct answer is “A”. The food will last for 100 days. Let us see how. According to the first condition, students consume food in 2 months, i.e. in 60 days. So this ratio would be 45:60

According to the second condition , the same amount of food is consumed by 27 students in x days. So that ratio would be 27:x. By Inverse Proportion ,

45 × 60 = 27 × x

x = (45 × 60) / 27

Question 3: What is the formula for the unitary method?

Answer: In case we are having the value of multiple items with us, then we will simply divide the total value with the number of units to get the value of 1 unit and this process is known as the unitary method.

Question 4: What is the unitary method for the percentage?

Answer: We can use the unitary method to find out 100 % of an amount given a percentage of that amount. For instance, if 10 % of an amount of money is Rs.23, then its 100 % is 10 × Rs.23 = Rs.230.

Question 5: What is the unitary ratio?

Answer: When one side of any ratio is one then the ratio is called a unitary ratio. This is useful while comparison.

Question 6: What is the unitary method in mathematics?

Answer: The unitary method is generally a way of finding out thesolution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value. However, this technique is useful for finding out the value of a unit from the value of a multiple, and therefore, the value of a multiple.

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4 responses to “Unitary Method”

Raj police exam me isse related questions aayenge kya sir?

Why the most part of this video in Hindi? How can students who doesn’t understand Hindi can make use of this training?

In 2nd question we have in that 22 months but in answer u told to take 2months why can’t 3months or 4,5

Wein the second question is for 22 months but in the answer you have given that we can take for 2 months which is 60 days so why can’t we take three months of four months of five months B

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Unitary Method: Formula and Solved Examples

The unitary method, in simple terms, is used to calculate the value of a single unit from a specified multiple. If the cost of 100 pens is Rs. 400, how do you calculate the cost of one pen? The unitary approach can be used to achieve arrive at the solution. Moreover, once the value of a single unit has been determined, the value of the needed units may be calculated by multiplying the single value unit. This approach is mostly used to calculate ratios and proportions.

By using the unitary method, we can find the missing value. For example, if 1 packet of milk costs ₹5, then what would be the cost of 3 such packets? We can easily calculate that, the cost of 3 packets is ₹15. Let us understand the concept in detail in this article.

What is Unitary Method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple. Unitary method in Hindi is known as ऐकिक नियम.

Ratio Proportion and Unitary Method

We use the unitary method to find the ratio of one quantity with respect to another quantity. To understand the concept of the unitary method formula in ratio and proportion , let us take an example.

Example: Akash’s income is $₹20000$ per month, and that of Arjun is $₹360000$ per annum. If the monthly expenditure of each of them is $₹10000$ per month, find the ratio of their savings.

Solution: Savings of Akash per month $ = ₹(20000 – 10000) = ₹10000$ Earning of Arjun in $12$ months $= ₹360000$ Income of Arjun per month $=\frac{360000}{12} = ₹ 30000$ Savings of Arjun per month $= ₹(30000-10000) = ₹ 20000$

Therefore, the ratio of savings of Akash and Arjun $= 10000 : 20000=1: 2$

Types of Unitary Method

In the unitary method, the value of a unit quantity is found first to calculate the value of the different number of units. It has two types of variations.

Direct Variation

Inverse Variation

In the direct variation, an increase in one quantity will cause an increase in another quantity; similarly, a decrease in one quantity will cause a decrease in another quantity. For instance, if the number of goods increases, their cost also increases.

Also, the amount of work done by one person will be less than the amount of work done by a group of people. Hence, if we increase the number of people, the work done will also increase.

Indirect Variation

It is the inverse of direct variation. Similar to inversely proportional. If the value of one quantity increases, then the value of another quantity decreases. For example, if we increase the speed, then we can cover the distance in less time. So, with an increase in speed, the time will decrease.

Unitary Method for Time and Work

Let’s take an example to understand the unitary method formula for time and work.

$“A”$ finishes his job in $15$ days, while $“B”$ takes $10$ days. In how many days will the same job be done if they work together? If $A$ takes $15$ days to finish his job then, $A’$s $1$ day of job $= \frac{1}{{15}}$

Similarly, $B’$s $1$ day of job $ = \frac{1}{{10}}$ Now, job is done by $A$ and $B$ in $1$ day $ = \frac{1}{{15}} + \frac{1}{{10}}$ Taking LCM $(15, 10)$, we have, $1$ day’s job of $A$ and $B = \frac{{(2 + 3)}}{{30}}$ $1$ day’s job of $(A + B) = \frac{1}{6}$

Thus, $A$ and $B$ can finish the job in $6$ days if they work together.

Unitary Method Questions

$10$ workers finish a job in $20$ hours. How many workers are required to finish the same work in $15$ hours?
If the annual rent of a house is $₹294000$, calculate the rent of $8$ months.
If $85$ pages weigh $17\,{\rm{g}},$ calculate the weight of $180$ pages.
If $5$ buses can carry $300$ people, find out the total number of people which $8$ buses can carry.
Rakesh completes $\frac{3}{4}$ of a job in $8$ days. How many extra days will he take to finish the job at his current rate?

Worksheet on Word Problems on Unitary Method

Word problems on the unitary method formula with the combination of questions on direct and indirect variation.

1. $6$ farmers harvest the crops in the field in $10$ hours. How many workers are required to do the same amount of work in $18$ hours?

2. $3$ men or $2$ women can earn $$192$ in a day. Find the earning of $7$ men and $5$ women in a day?

3. The weight of $56$ pages is $8\,{\rm{g}}.$ What is the weight of $150$ such pages? How many such pages weigh $5\,{\rm{g?}}$

4. Meera types $400$ words in $30$ minutes. How many words would she type in $7$ minutes?

5. A man is paid $₹750$ for $6$ day’s work. If he works for $28$ days, how much will he get?

6. A tank of water can be filled in $7$ hours by $5$ equal-sized pumps working together. How much time will $8$ pumps take to fill it up?

7. $15$ workers can build the wall in $20$ days. How many workers will build the wall in $12$ days?

8. $76$ men can complete the work in $42$ days. In how many days will $56$ men do the same work?

9. In a camp, there are provisions for $400$ persons for $23$ days. If $60$ more persons join the camp, find the number of days the provision will last?

10. If $10$ workers working for $4$ hours complete the work in $12$ days, in how many days will $8$ workers working for $6$ hours complete the same work?

11. The freight for $75$ quintals of goods is $₹375$. Find the freight for $42$ quintals.

12. A truck travels ${\rm{150\,km}}$ in $3$ hours.

(a) How long will it take to travel $912\,{\rm{km?}}$

(b) How far will it travel in $10$ hours?

Real-Life Applications of Unitary Method

The unitary method is very much helpful in solving various problems that we come across in our day-to-day life. Some of the real-life applications of the unitary method are:

To find the speed of a vehicle for a given distance, if the speed and distance are given in different quantities.
To find the number of men required to complete a given amount of work.
To find the area of a square of a given length if the ratio of its area and side is given.
To find the cost of a certain number of objects, if the cost and number of objects are given in different quantities.
To find the percentage of a quantity.

Solved Examples – Unitary Method Formula

(Includes Unitary Method Problems and Unitary Method Questions for Competitive Exams)

Q.1. Rupali can type $540$ words in $30$ minutes. How many words will she able to type in $20$ minutes with the same efficiency? Ans: Number of words typed in $30\,\min = 540.$ The number of words typed in $1\;{\rm{min}} = \frac{{540}}{{30}} = 18$ Therefore, the number of words typed in $20\,\min = 20 \times 18 = 360.$ Hence, Rupali will be able to type $360$ words in $20$ minutes.

Q.2. If $45$ students can consume a stock of food in $2$ months, then for how many days the same stock of food will last for $27$ students? Ans: The food will last for $100$ days. Let us see how. According to the first condition, students consume food in $2$ months, i.e., in $60$ days. So this ratio would be $45 : 60$ According to the second condition, the same amount of food is consumed by $27$ students in $x$ days. So that ratio would be $27: x $. By Inverse Proportion, $45×60=27×x$ $ \Rightarrow x = \frac{{\left( {45 \times 60} \right)}}{{27}}$ $ \Rightarrow x = 100$

Q.3. The cost of $8$ apples is $₹ \, 120$. Find the number of apples that can be purchased with $₹ \, 240$. Ans: Given, the cost of $8$ apples $=₹ \, 120$. Hence the cost of $1$ apple $=₹\, 15.$ Now, the number of apples that can be purchased in $₹\, 15=1.$ The number of apples that can be purchased with $₹1 = \frac{1}{{15}}$. Hence, the number of apples that can be purchased with $₹240 = \frac{1}{{15}} \times 240 = 16$ apples.

Q.4. Rohan goes to a stationery shop to buy some books. The shopkeeper informs him that $2$ books would cost $$90$. Can you find the cost of $5$ books with the help of the unitary method? Ans: The number of books corresponds to the “unit”, and the cost of the books corresponds to the “value”. Let’s solve it step-wise. Step 1: First, we will find the cost of $1$ book. Cost of $1$ book $= \frac{{{\rm{ Total \, cost \, of \, books }}}}{{{\rm{ Total \, number \, of \, books }}}} = \frac{{90}}{2} = 45.$ Step 2: Now, we will find the cost of $5$ books. Cost of $5$ books $=$ Cost of $1$ book $\times $ Number of books $=45×5=225.$ Therefore, the cost of $5$ books is $$225$.

Q.5. A car travelling at a speed of ${\rm{140\,kmph}}$ covers ${\rm{420\;km}}$. How much time will it take to cover ${\rm{280\;km}}$? Ans: First, we need to find the time required to cover ${\rm{420\;km}}.$ ${\rm{Speed = }}\frac{{{\rm{ Distance }}}}{{{\rm{ Time }}}}$ $ \Rightarrow 140 = \frac{{420}}{T}$ $ \Rightarrow T = 3$ hours Applying the unitary method, we get, To travel ${\rm{420\;km}},$ the time required is $3$ hours So, to travel $1\,{\rm{km}},$ the time required is $\frac{3}{{420}}$ hours Hence, to travel ${\rm{280\;km}}$, the time required is $\frac{3}{{420}} \times 280 = 2$ hours

Unitary method in maths is a method by which we can find the value of one unit from the value of many units and the value of many units from the value of one unit. It is a method that we use for the majority of the calculations in Mathematics. You will find this method helpful while solving problems on ratio and proportion, geometry, algebra etc.

Here, in this article, we learnt the definition of the unitary method with an example. We understood the technique involved in solving the problems related to the unitary method of converting the value of many to a single unit and the value of a single unit to the value of many units. We came through the types of unitary methods and understood direct and inverse variation.

We also studied the relation between ratio proportion and the unitary method. This article provides a worksheet related to the unitary method that helps understand different examples applicable in daily life. Solved examples mentioned in this article will be helpful in taking competitive examinations.

FAQs on Unitary Method

Following are the frequently asked questions on unitary method in maths:

Q.1. What is the formula of the unitary method? Or what is unitary law? Ans: The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit by the number of units to get the necessary value.

Q .2 . How do you solve a unitary problem? Ans: The unitary method is a method for solving a problem by first finding the value of one unit and then finding the unknown value by multiplying the one unit value.

Q .3 . What are the applications of the unitary method? Ans: Practical applications of the unitary method are many. It is applicable in problems related to distance, time, work, speed, ratio and proportion. It can be used to calculate the cost of goods or to establish their pricing based on local and global market trends.

Q.4. What are the two types of unitary methods? Ans: The unitary method is mainly dependent on ratio and proportion. But depending on the value and quantity of a unit to be primarily calculated, there are two types of variations: 1. Direct variation 2. Inverse variation

Q.5. How to teach the unitary method to students? Ans: Let us take an example in which we need to find the price of $50$ shirts if the price of $8$ shirts is given to us as $₹800$. In this case, we will first find the price of $1$ shirt and multiply it by $50$. Therefore, price of $1$ shirt $ = \frac{{800}}{8} = ₹100$ Price of $50$ shirts $=50×100=₹ 5000.$ Hence, we got the price of $50$ shirts using the unitary method.

We hope this article on the unitary method has provided significant value to your knowledge. Embibe wishes you the best of luck!

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Unitary Method

Trigonometry.

In simple terms, the unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit. This method is majorly used for ratio and proportion concept.

What is Unitary Method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units. What can units and values be?

Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value. While solving a problem using the unitary method, it is important to recognize the units and values.

For simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side. In the above problem, we know the amount of the number of apples and the value of the apples is unknown. It should be noted that the concept of ratio and proportion is used for problems related to this method.

Example of Unitary Method

Consider another example; a car runs 150 km on 15 litres of fuel, how many kilometres will it run on 10 litres of fuel?

In the above question, try and identify units (known) and values (unknown).

Kilometre = Unknown (Right Hand Side)

No of litres of fuel = Known (Left Hand Side)

Now we will try and solve this problem.

15 litres = 150 km

1 litre = 150/15 = 10 km

10 litres = 10 x 10 = 100 km

The car will run 100 kilometres on 10 litres of fuel.

Unitary Method in Ratio and Proportion

If we need to find the ratio of one quantity with respect to another quantity, then we need to use the unitary method. Let us understand with the help of examples.

Example: Income of Amir is Rs 12000 per month, and that of Amit is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9960 per month, find the ratio of their savings.

Solution: Savings of Amir per month = Rs (12000 – 9960) = Rs 2040

In 12 month Amit earn = Rs.191520

Income of Amit per month = Rs 191520/12 = Rs. 15960

Savings of Amit per month = Rs (15960 – 9960) = Rs 6000

Therefore, the ratio of savings of Amir and Amit = 2040:6000 = 17:50

Types of Unitary Method

In the unitary method, the value of a unit quantity is calculated first to calculate the value of other units. It has two types of variations.

Direct Variation

Inverse Variation

In direct variation, increase or decrease in one quantity will cause an increase or decrease in another quantity. For instance, an increase in the number of goods will cost more price.

Also, the amount of work done by a single man will be less than the amount of work done by a group of men. Hence, if we increase the number of men, the work will increase.

Indirect Variation

It is the inverse of direct variation. If we increase a quantity, then the value of another quantity gets decrease. For example, if we increase the speed, then we can cover the distance in less time. So, with an increase in speed, the travelling time will decrease.

Applications of Unitary Method

The unitary method finds its practical application everywhere ranging from problems of speed, distance, time to the problems related to calculating the cost of materials.

The method is used for evaluating the price of a good.
It is used to find the time taken by a vehicle or a person to cover some distance in an hour.
It is used in business to determine profit and loss.

Unitary Method Speed Distance Time

Let us take unitary method problems for speed distance time and for time and work.

Illustration : A car travelling at a speed of 140 kmph covers 420 km. How much time will it take to cover 280 km?

Solution : First, we need to find the time required to cover 420 km.

Speed = Distance/Time

140 = 420/T

T = 3 hours

Applying the unitary method,

420 km = 3 hours

1 km = 3/420 hour

280 km = (3/420) x 280 = 2 hours

Unitary Method For Time and Work

Example: “A” finishes his work in 15 days while “B” takes 10 days. How many days will the same work be done if they work together?

If A takes 15 days to finish his work then,

A’s 1 day of work = 1/15

Similarly, B’s 1 day of work = 1/10

Now, total work is done by A and B in 1 day = 1/15 + 1/10

Taking LCM(15, 10), we have,

1 day’s work of A and B = (2+3)/30

1 day’s work of (A + B) = ⅙

Thus, A and B can finish the work in 6 days if they work together.

Unitary Method Questions

12 workers finish a job in 20 hours. How many workers will be required to finish the same work in 15 hours?
If the annual rent of a flat is Rs. 3600, calculate the rent of 7 months.
If 56 books weigh 8 Kg, calculate the weight of 152 books.
If 5 cars can carry 325 people, find out the total number of people which 8 cars can carry.
Rakesh completes 5/8 of a job in 20 days. How many more days will he take to finish the job at his current rate?

Frequently Asked Questions – FAQs

What is the unitary method, what are the types of unitary method, what is the formula of the unitary method, how to solve the unknown using the unitary method, what is the unitary method of percentage.

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Unitary Method

Unitary Method – Definition

The unitary method is a fundamental concept of Mathematics and makes it convenient to solve various sums. This method generally involves finding the value of a unit in the given terms, using which the value of the given quantity of units can be calculated. The following example will help you understand the terms ‘unit’ and ‘value’. You buy 7 juicy apples from your local grocery shop. The shopkeeper puts up an offer of purchasing 10 apples for Rs 100. In this situation, the ‘units’ are the apples and the ‘value’ is the price of the apples.

It is important to recognize and familiarize the terms of units and values when using the unitary method in your sums.

(Image will be uploaded soon)

A simple tip is to write the values to be calculated on the right-hand side and known values on the left-hand side. The problem present above clearly indicates the number and total price of apples as unknown. At this point, the use of ratio and proportions come into the picture.

Concept Behind Unitary Method

The unitary method concept helps us to pick out a single value from a multiple set of values having different properties. For Instance, the price of 40 pens is Rs. 400, how do we calculate the price of a single pen?

This can be done using the unitary method. After finding the value of a single pen, we calculate the value of the required number of pens. This is done by multiplying the value of the single unit by the given number of units.

Example of Unitary Method Problems

While going through a variety of sums to understand the unitary method, be sure to pay attention to the items in the given set of data. Given below are some of the common unitary method sums.

Let us consider the following example. A car runs 150 km on 15 liters of fuel, how many kilometers will it run on 10 liters of fuel?

First, we try to identify our quantities,

Here, the units are known, however, the values are unknown.

Kilometer = Unknown (Place in the Right Hand Side)

No of liters of fuel = Known (place in the Left Hand Side)

15 litres = 150 km

1 litre = 150/15 = 10 km

10 litres = 10 х 10 = 100 km

Therefore, the car can run 100 kilometers on 10 liters of fuel.

Unitary Method in Time and Work

The unitary method uses the properties of time and works in the relevant numerical problems.

Let us consider the following example. Desmond finishes his work in 15 days while Betty takes 10 days. Find the number of days it will take them to complete the same work together?

If Desmond takes 15 days to finish his work then,

Desmond’s 1 day of work =1/15

Betty’s 1 day of work = 1/10

Now, the total work is done be Desmond and Betty in 1 day = 1/15 + 1/10

Taking the LCM (15, 10),

1 day’s work of Desmond and Betty = 2+3/30

1 day’s work of (Desmond + Betty) = 1/6

Thus, if Desmond and Betty work together, they can complete the work in 6 days.

Ratio and Proportion in Unitary Method

The concepts of ratio-proportion and unitary method are inter-linked. The majority of the sums in ratio and proportion exercises are based on fractions. A fraction is represented as a:b. The terms ‘a’ and ‘b’ can be any two integers.

To find the ratio of one quantity for another requires the use of the unitary method.

Consider the following example. The income of Ajay is Rs 12000 per month, and that of Bob is Rs 191520 per annum. If the monthly expenditure for each is Rs 9960 per month, express their savings in terms of ratios.

The savings of Ajay per month = Rs (12000 - 9960) = Rs 2040

In 12 months, Bob earns = Rs.191520

The Income of Bob per month = Rs 191520/12 = Rs. 15960

The savings of Bob per month = Rs(15960 - 9960) = Rs 6000

Therefore, the ratio of savings of Ajay and Bob = 2040 : 6000 = 17 : 50

FAQs on Unitary Method

1. What are the Two Types of Unitary Methods?

The unitary method greatly relies on the concept of ratio and proportions. But, depending on the value and quantity of a unit to be primarily calculated, there are two types of variations found.

Direct Variation - There is an increase or decrease in one quantity and this reflects on the increase or decrease in the next quantity.

For example, the increase in the number of goods will hike up the price. The amount of work done by a group of men is relatively higher than that of a single man.

Inverse Variation - The inverse of direct variation results in inverse variation. The quantity of two sets is inversely proportional, that is, one increase results in the decrease of the other.

For instance, when speed increases, more distance is covered in less time.

2. What are the Applications of the Unitary Method?

The practical applications of the unitary method are vast. It is used for solving complex problems in Mathematics. This involves the sums of speed, distance, time, work, ratio, and proportions. To some extent, it aids in the realm of Finance as well. It can be used to calculate the cost of goods or to establish their pricing based on the local or global market trends.

It can be used to determine the profit and loss attained by a company. The most common problems solved by the unitary method uses the concept of distance covered and time taken by different transportation systems.

When you buy things like veggies in your daily life, the merchant always specifies the wholesale rates. Let's say you spend 250 rupees on 5 kilograms of rice. How can you determine the price of a unit kilogram of rice? The unitary approach is the answer to this. Furthermore, given the cost of a single unit, you may use this to compute the price of numerous units.

Let us learn about the unitary technique because of its importance in our daily lives.

A single or individual unit is referred to as unitary. As a result, the goal of this method is to determine values about a single unit. For example, if a bike travels 60 kilometres on two litres of petrol, you can use the unitary technique to calculate how many kilometres it will go on one litre of petrol.

The unitary method, in other words, is the process by which we determine the value of one unit and then utilise it to determine the value of numerous units. Let's look at an example of how the unitary approach is used:

Assume, Rahul spends 120 Rs on a dozen bananas. This implies that 12 bananas are worth 120 rupees. 1 banana costs 120/12 = 10 rupees. As a result, a single banana costs ten rupees. Let's say you need to calculate the cost of 24 bananas. This can be done as follows: 1 banana costs 10 rupees; 24 units will cost 240 rupees.

In other words, if you are given the value of several goods, you simply divide the total value by the number of units to get the value of one unit. The unitary technique is what it sounds like.

Let's now solve some questions to understand the concept of the unitary method.

3. The price of ten pens is Rs. 50. Find the maximum number of pens that can be bought for 100 Rs.

The cost of ten pens is estimated to be 50 rupees. As a result, the price of a pen is 5 rupees. Now,

The number of pens that can be purchased for 100 rupees equals to 20.

4. What is the unitary method's formula?

If we have the value of numerous objects with us, we can simply divide the total value by the number of units to get the value of one unit, which is called the unitary technique.

5. What is the percentage unitary method?

The unitary approach can be used to find 100 percent of an amount given a percentage of it. For example, if 50% of a sum of money is Rs. 40, then its 100% is (100/50) × 40 = Rs. 80

6. What is the unitary ratio?

When one side of a ratio is one, the ratio is referred to as a unitary ratio. This comes in handy when comparing two things.

7. How is the unitary method defined in terms of mathematics?

The unitary method is a method of determining the answer to a problem by first determining the value of a single unit and then multiplying the single unit value by the essential value. This technique, on the other hand, is useful for determining the value of a unit from the value of a multiple, and thus the value of a multiple.

8. How can I understand the concept of the unitary method?

The concept of the unitary method is very easy to understand as you first have to find the value of a unit from a given problem. In the above article, we have provided a lot of examples that will help you to understand the concept of the unitary method very easily. You will also find the definitions of all the terms that are related to the unitary method.

9. What are the various examples where the unitary method can be applied?

The unitary method can be applied to two sets of examples viz; examples revolving around indirect variations and examples revolving around direct variations. In both types of variations, you can find the value of the single unit. To find the value of that single unit, you first have to figure out whether the problem is related to direct variation or indirect variation.

Unitary Method Worksheet

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Help your students prepare for their Maths GCSE with this free unitary method worksheet of 33 questions and answers

Section 1 of the unitary method worksheet contains 24 skills-based unitary method questions, in 3 groups to support differentiation
Section 2 contains 5 applied unitary method questions with a mix of word problems and deeper problem solving questions
Section 3 contains 4 foundation and higher level GCSE exam style unitary method questions
An answer key and a mark scheme for all unitary method questions are provided
Questions follow variation theory with plenty of opportunities for students to work independently at their own level
All questions created by fully qualified expert secondary maths teachers
Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Unitary method at a glance

The unitary method is a method that involves finding the value of a single unit and using that to find the value of a different number of units of something. For example, if a factory produces 3000 tubes of toothpaste in 4 days, we can find the number of tubes of toothpaste produced in 5 days using the unitary method . First we calculate the number of tubes of toothpaste in 1 day, 3000 divided by 4 = 750. We can then multiply by 5 to find the number produced in 5 days: 750 times 5 = 3750.

The above example has two variants with direct variation , commonly referred to as direct proportional. The unitary method can also be used for problems involving indirect variation (inverse proportion). For example, if a project is 6 days work for 3 people, we can work out how many days work it would be for 2 people. First, we find the number of days for 1 person, 6 times 3 = 18. We can then divide by 2 to find the number of days for 2 people: 18 divided by 2 = 9.

Looking forward, students can then progress to additional ratio and proportion worksheets , for example a ratio worksheet or a simplifying and equivalent ratios worksheet .

For more teaching and learning support on Ratio and Proportion our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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Unitary Method Questions

Unitary method questions with solutions are given here for students to practice and understand the concept of the unitary method. The unitary method is a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Learn more about Unitary Method .

Types of Unitary Method:

	The value of multiple units increases with an increase in the number of units.
	The value of multiple units decreases with an increase in the number of units or vice-versa.

Video Lesson on Unitary Method

Unitary Method Questions with Solutions

Following are some questions on unitary method of direct variation type.

Question 1: If the price of 5 kg potato is ₹ 150. Find the value of 24kg potato.

Price of 5 kg potato = ₹ 150

Price of 1kg potato = ₹ 150/5 = ₹ 30

Price of 24 kg potato = 24 × 30 = ₹ 720

Question 2: A pack of 120 soaps is ₹ 540. Find the cost of 12 soaps.

Cost of 120 soaps = ₹ 540

Cost of 1 soap = ₹ 540/120 = ₹ 4.5

Cost of 12 soaps = 4.5 × 12 = ₹ 54

Question 3: The length of the shadow of a 168 cm tall person at a particular time of day is 252 cm. What will be the length of the shadow of a 158 cm tall person at the same time of the day?

Length of shadow for 168 cm = 252 cm

Length of the shadow for 1 cm = 252/168 = 1.5 cm

Length of the shadow for 158 cm = 1.5 × 158 = 237 cm.

Therefore, the length of the shadow for a 158 cm tall person is 237 cm.

Question 4: An iron rod of uniform thickness of length 5.6 m weighs 2.4 kg. How much will be the weight of 5 iron rods of the same thickness and length 8.4 m?

Weight of 5.6 m rod = 2.4 kg

Weight of 1 m rod = 2.4 / 5.6 = 3/7 kg

Weight of 8.4 m rod = 3/7 × 8.4 = 3.6 kg

Weight of 5 such rods = 5 × 3.6 kg = 18 kg.

Question 5: The extension produced in an elastic wire on suspension of 94 kg weight is 2.24 m. What will be the extension produced in the wire of the same material when 72 kg weight is suspended?

Extension produced on suspension of 94 kg weight = 0.47 m

Extension produced on suspension of 1 kg weight = 0.47/94 = 0.005 m

Extension produced on suspension of 72 kg weight = 0.005 × 72 = 0.36 m.

Also, Read:

Ratio and Proportion
Direct and Inverse Proportion
Simple Interest
Compound Interest

Now, we shall solve some unitary method questions based on the inverse variation.

Question 6: 15 men can work together to finish a piece of work in 25 days. How many days will 20 men take to complete that same piece of work?

Clearly, it is a case of inverse variation.

Number of days 15 men take to complete the work = 25 days

Number of days 1 man takes to complete the work = (25 × 15) = 375 days

Number of days 20 men take to complete the work = 375/20 = 18.75 ≈ 19 days

∴ 20 men will take approximately 19 days to complete the work.

If M persons can finish a W units of work in D days working H hours a day and M persons can finish the W units of work in D days working H hours a day, then

Question 7: To complete a certain task 15 men take 10 days working 12 hours a day. How many hours a day should 10 men work to complete the same task in 20 days?

Total work done by 15 men in 10 days working 12 hours a day = 15 × 10 × 12.

Let 10 men complete the task in 20 days working h hours a day.

Total work done by 10 men in 20 days working h hours a day = 10 × 20 × h

But, 15 × 10 × 12 = 10 × 20 × h

⇒ h = (15 × 10 × 12)/(10 × 20)

∴ 10 men should work 9 hours a day to complete the task in 20 days.

Question 8: At a construction site, 4 men or 5 women can complete a task in 82 days. How many days will it take to complete the task by 5 men and 4 women?

Let x be the work done by one man and y be the work done by one woman.

Then according to the question,

Now, 5x + 4y = 5(5y/4) + 4y = 25y/4 + 4y

If 5y can complete the task in 82 days

Then, 41y/4 can complete the task in 5y × 82 × 4/41y = 40 days.

∴ 5 men and 4 women can complete the task in 40 days.

Question 9: Two taps, A and B, can fill an empty tank in 30 hours and 15 hours, respectively. They both were turned on to fill the tank, but tap A was turned off after some time, and tap B took 12 hours to fill the tank. Find out after how much time tap A was turned off?

Time taken by tap A to fill the tank = 30 hours

Portion of the tank filled by tap A in 1 h = 1/30

Time taken by tap B to fill the tank = 15 hours

Portion of the tank filled by tap B in 1 h = 1/15

Now, tap B ran for 12 hours, let tap A ran for x hours, then

x/30 + 12/15 = 1

⇒ x/30 + 24/30 = 1

⇒ x + 24 = 30

⇒ x = 30 – 24 = 6 hours.

∴ after 6 hours tap was turned off.

Question 10: A group of 120 men had provisions for 200 days. After 5 days, 30 men left. How long the provisions will last for the remaining men?

According to the question,

The remaining provision is sufficient for 120 men up to 195 days.

Number of days provision for 1 man = 195 × 120 days

Number of days provision for (120 – 30) = 90 men = (195 × 120)/90 = 260 days

The provisions will last for 260 days.

Practice Questions on Unitary Method

1. A herd of 45 cattle can graze a field in 13 days. How many of them can graze the same field in 9 days?

2. If 35 meters of cloth costs ₹ 1250. What will be the cost of 13 meters of the same cloth?

3. Travelling cost by bus for 125 km is ₹ 1050. How much will be the cost of travelling for 45 km?

4. A garrison had provision for 1500 men for 30 days. After some days, 300 more men joined the garrison. How many days the provisions will last?

5. Five men or ten women can complete a job in 20 days. In how many days can 3 men and 4 women can complete the same job?

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Worksheet on Word Problems on Unitary Method

Worksheet on word problems on unitary method provides mixed questions on direct variation and indirect variation.

1. 12 farmers harvest the crops in the field in 20 hours. How many workers will be required to do the same work in 15 hours?

2. 2 men or 3 women can earn $192 in a day. Find how much 5 men and 7 women will earn in a day?

3. The weight of 56 books is 8 kg. What is the weight of 152 such books? How many such books weigh 5 kg?

4. John types 450 words in half an hour. How words would he type in 7 minutes?

5. A worker is paid Rs.750 for 6 days’ work. If he works for 23 days, how much will he get?

6. A water tank can be filled in 7 hours by 5 equal sized pumps working together. How much time will 7 pumps take to fill it up?

7. 15 masons can build the wall in 20 days. How many masons will build the wall in 12 days?

8. 76 persons can complete the job in 42 days. In how many days will 56 persons do the same job?

9. In a camp, there are provisions for 400 persons for 23 days. If 60 more persons join the camp, find the number of days the provision will last?

10. If 10 workers, working for 4 hours complete the work in 12 days, in how many days will 8 workers working for 6 hours complete the same work?

11. The freight for 75 quintals of goods is Rs. 375. Find the freight for 42 quintals.

12. A car travels 228 km in 3 hours.

(a) How long will it take to travel 912 km?

(b) How far will it travel in 7 hours?

Answers for the worksheet on word problems on unitary method of direct variation and inverse variation are given below to check the exact answers of the above problems.

1. 16 farmers

3. 21 5/7 kg, 35 books

4. 105 words

10. 10 days

12. (a) 12 hours

(b) 532 km

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Inverse Variation Using Unitary Method Worksheet on Inverse Variation Using Method of Proportion

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Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

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Unitary Method

The unitary method is a fundamental technique in mathematics that is used to solve problems related to finding the value of a single unit and then using it to find the value of multiple units. This method is especially useful in problems involving ratios, proportions, and rates.

It’s a simple and effective way to tackle problems involving ratios and proportions , especially when dealing with real-world scenarios like shopping, travel, and others.

Table of Content

What is Unitary Method?

Examples of unitary method, how to use the unitary method, types of unitary method, applications of unitary method, sample problems on unitary method, practice questions on unitary method.

Unitary Method is a fundamental approach in mathematics used to solve problems related to finding the value of a single unit and then the value of multiple units. It’s based on the concept of proportionality , which means if one quantity increases or decreases, the other does so in a direct or inverse proportion.

This is explained with examples, suppose a car runs 15 km in one litre of petrol then it will run 150 km in 10 litres of petrol. Here, the distance covered by car directly increases with increase in petrol consumption, (assuming initial condition are same).

Unitary method is named so because it focuses on finding the value of one unit first.

Few examples where unitary method are used are added below

Cost of one apple will be $10/5 = $2
Car travel in 3 hours = 60 × 3 = 180 km

Here’s a step-by-step approach to using the unitary method:

Step 1: (Identify the Unit) Recognize what one unit represents in the problem. It could be one apple, one hour of travel, or one liter of paint.
Step 2: (Relate the Unit to a Known Value) Look for the information given about a specific number of units. This could be the cost of 5 apples, the distance traveled in 2 hours, or the amount of paint needed to cover a certain area.
Step 3: (Find the Unit Value) Divide the known value (from step 2) by the number of units it represents. This gives you the cost of one apple, the speed traveled per hour, or the amount of paint needed per unit area.
Step 4: (Calculate the Desired Value) Once you have the unit value, multiply it by the desired number of units to find the answer.

There are two main types of unitary method problems:

Direct Variation

Inverse variation.

In mathematics, direct variation refers to a relationship between two quantities where one quantity changes in direct proportion to the other. Specifically:

Definition: Two quantities are said to be in direct proportion if an increase in one quantity leads to an increase in the other quantity, provided their respective ratios remain the same.

Equation: In direct variation, we express the relationship as y = kx, where:

y represents the dependent variable (the one that changes).
x represents the independent variable (the one that remains constant or is controlled).
k is the constant of proportionality .

Example 1: Cost of Apples

Suppose you’re buying apples at a grocery store. The cost of apples varies directly with the number of apples you purchase. If the cost of 5 apples is $10, we can set up a direct variation equation:

Solving for k, we find that k = 2. Therefore, the cost of x apples can be expressed as

Example 2: Work Completion

Suppose two workers, A and B, can complete a particular job together. Their work rates vary directly with the number of workers. If A and B together can complete the job in 72 days, we can set up a direct variation equation:

(1/72) = (1/x) + (1/y)

where x represents the number of days A alone can complete the job, and y represents the number of days B alone can complete the job. Solving for x, we find that x = 120. Therefore, A alone can complete the job in 120 days.

Inverse variation, on the other hand, describes a relationship where one quantity increases as the other decreases, and vice versa. Specifically:

Definition: Two quantities are said to be in inverse proportion if an increase in one quantity leads to a decrease in the other quantity, provided their product remains constant.

Equation: In inverse variation, we express the relationship as xy = k, where:

x and y are the variables.
k is the constant of proportionality.

Example 1: Pressure and Volume

Consider a gas in a container. The pressure of the gas varies inversely with the volume of the container. If the pressure is 10 atm when the volume is 2 liters, we can set up an inverse variation equation:

Solving for k, we find that k = 20. Therefore, the pressure (P) when the volume (V) is x liters can be expressed as:

Remember that direct variation involves a constant ratio, while inverse variation involves a constant product.

Various application of Unitary Methods are added below as:

Unitary Method in Ratio and Proportion

Unitary Method helps in solving problems where the ratios of two quantities are given, and we need to find the value of one of the quantities. It forms the foundation for understanding ratios and proportions, where you compare quantities of different units.

Unitary Method in Speed Time and Distance

It is used to calculate the speed, time, or distance when any two of these three variables are known. The unitary method helps solve problems involving speed, time, and distance, all interrelated concepts.

Unitary Method in Rates and Percentages

Unitary method is used to find rates (cost per unit) and calculate percentages based on unit values.

Operations of Integers
Subtraction of Decimal
Sum – Definition, Examples & Formulas
Additive Identity vs Multiplicative Identity

Problem 1: If 3 oranges cost $2.10, how much does 1 orange cost?

Identify Unit: One orange Relate Unit to a Known Value: We know the cost of 3 oranges ($2.10). Find Unit Value: Unit value (cost of 1 orange) = $2.10 / 3 oranges = $0.70 per orange. Calculate Desired Value: The question asks for the cost of 1 orange, which we already found as $0.70.

Problem 2: A car travels 120 km in 2 hours. What is the speed of the car?

Identify Unit: Speed is measured in kilometers per hour (km/h). So, our unit is 1 hour. Relate Unit to a Known Value: We know the distance traveled in 2 hours (120 km). Find Unit Value: Speed (per hour) = Total distance / Time taken = 120 km / 2 hours = 60 km/hour. Calculate Desired Value: Question asks for the speed, which we found as 60 km/hour.

Problem 3: A recipe requires 2 cups of flour for 8 cupcakes. How many cups of flour are needed for 12 cupcakes?

Identify Unit: One cupcake Relate Unit to a Known Value: We know the amount of flour required for 8 cupcakes (2 cups). Find Unit Value: Flour per cupcake = Total flour / Number of cupcakes = 2 cups / 8 cupcakes = 0.25 cups per cupcake. Calculate Desired Value: We need to find the flour for 12 cupcakes. Flour Required = Unit value (flour per cupcake) × Number of cupcakes Flour Required = 0.25 cups/cupcake × 12 cupcakes = 3 cups.

Problem 4: If 7 meters of cloth cost $14, what is the cost of 3 meters of cloth?

Identify Unit: One meter of cloth Relate Unit to a Known Value: We know the cost of 7 meters of cloth ($14). Find Unit Value: Cost per meter = Total cost / Number of meters = $14 / 7 meters = $2 per meter. Calculate Desired Value: Cost of 3 meters = Unit value (cost per meter) × Number of meters = $2/meter × 3 meters = $6.

Problem 5: A painter needs 5 liters of paint to cover 20 square meters of wall. How much paint is needed to cover 10 square meters?

Identify Unit: Paint needed per square meter Relate Unit to a Known Value: We know the paint needed for 20 square meters (5 liters). Find Unit Value: Paint per square meter = Total paint / Area covered = 5 liters / 20 square meters = 0.25 liters per square meter. Calculate Desired Value: Paint needed for 10 square meters = Unit value (paint per square meter) × Area to be covered = 0.25 liters/square meter × 10 square meters = 2.5 liters.

Problem 6: A train travels 360 km in 6 hours. At what speed will it cover 240 km?

I dentify Unit: Speed (km/h) – We can find the speed in 1 hour and then use it for any time duration. Relate Unit to a Known Value: We know the distance traveled in 6 hours (360 km). Find Unit Value: Speed (per hour) = Total distance / Time taken = 360 km / 6 hours = 60 km/hour. Calculate Desired Value: Since we already found the speed as 60 km/h, this speed will also apply to cover 240 km. The train will cover 240 km at 60 km/hour.

Note: Unitary method is useful for both direct and inverse proportion problems. In problem 6, even though distance reduces (inverse proportion to time), the speed (unit value per hour) remains constant.

Q1. If 3 kg of rice costs $27, find the cost of 5 kg of rice.

Q2. A cyclist covers a distance of 45 km in 3 hours. Calculate the speed of the cyclist.

Q3. 7 meters of cloth cost $14. What is the cost of 3 meters of cloth?

Q4. A recipe requires 2 cups of flour for 8 cupcakes. How many cups of flour are needed for 12 cupcakes?

Q5. A bus travels 480 km in 8 hours. How long would it take to travel 360 km?

Unitary Method – FAQs

Unitary Method is a technique used to find the value of a single unit from the value of a multiple units and vice versa.

When do we use the Unitary Method?

It is used in problems involving ratios, proportions, and relationships between two quantities.

Can the Unitary Method be used for complex problems?

Yes, it can be applied to more complex problems as long as the relationship between the quantities is proportional.

What is an example of the Unitary Method in daily life?

Calculating the price per unit when shopping or determining the cost of fuel per mile are common examples.

Are there limitations to the unitary method?

For complex problems with multiple variables, algebraic methods might be more efficient.

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What is Unitary Method? Worksheets and Problems of Unitary Method (PDF)

What is the unitary method.

The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result. The unitary method is widely used in mathematics to solve word problems of various kinds like algebra, ratio, proportions, geometry, etc. The word unitary itself means individual or single unit.

Example’s of the Unitary Method

Example Problem: If the cost of 12 pens is $36. What is the price of 7 pens?

Rules of Unitary Method

As shown in the above example, the problem solving using the unitary method is very simple. Simply follow the following rules

Rule 1: Keep the required answer on the right side

The cost of 12 pens is $36 Hence, the Cost of 1 pen=36/12=$3 (division) So, the cost of 7 pens is 7*3=$21 (multiplication)

Rule 2: Ask a question to find if you expect an increase or decrease of value when you wish to know the value of unit quantity.

In maximum of the cases, when finding the value of unit quantity the factor will decrease and thus division will happen as explained in the above examples. Means if the cost of 12 pens is $36. So, the price of 1 pen will reduce and thus division has to be performed. But there will be situations when this may not be true. The unitary method problems related time and resources usually does not follow the same. Look at the example given below:

12 men can do the job in 24 days. So, 1 man can do the same job in 12X24 days (multiplication) Hence, 6 men will do the job in (12*24)/6=48 days (division).

Unitary Method Worksheet

Q1. unitary method worksheet 1: multiple choice questions.

Use the unitary method to find out the correct answers from the given options.

Q3. A factory produces 75 masks in 5 hours. If it operates 8 hours daily, how many masks does it produce in a week?

Q6. The annual rent of a building is Rs. 48000. Find the rent for 7 months?

Q9. Shalini bought one dozen bananas at Rs. 60. Find the cost of one banana?

Q2. Unitary method worksheet 2: Word problems

B. If 15 chocolates cost Rs. 225. How many chocolates Advik can buy with Rs. 150?

E. 15 books contain 3375 pages. So, what will be the number of pages for 21 such books?

H. A clock loses 15 seconds in 10 hours; how much does it lose in 2 days?

UNITARY METHOD WITH FRACTIONS

If 4/7 of an amount of money is $480, then 1/7 of the amount is

= $480 ÷ 4

= $120

Thus 6/7 of the amount = 6x $120 = $720.

and 7/7 is the whole amount which is 7 x $120 = $840.

So, given the value of a number of parts of a quantity we can find one part of the quantity and then the whole quantity or another fraction of the quantity. This is called the unitary method.

Example 1 :

If 3/8 of a shipping container holds 2100 identical cartons, how many cartons will fit into :

(a) 5/8 of the cartons

(b) the whole container

Given that :

3/8 of a shipping container holds 2100 identical cartons.

Let us find the number of identical cartons that 1/8 of shipping container hold.

1/8 of shipping container can hold = 2100/3

= 700 cartons

(i)

Number of identical cartons that 5/8 of shipping container will hold

= 700(5)

= 3500 cartons

(ii) 8/8 of container can hold = 700(8)

= 5600

Example 2 :

2/11 of Jo’s weekly earnings are paid as income tax. She has $666 remaining after tax. What is her total weekly pay?

Let x be Jo's weekly income.

2/11 of his earning are paid as income.

Remaining amount = 666

x - (2/11) of x = 666

x-(2x/11) = 666

9x/11 = 666

x = 666 ⋅ (11/9)

x = 814

So, Jo's weekly earning is $814.

Example 3 :

3/ 13 of a field was searched for truffles and 39 were found. How many truffles would we expect to find in the remainder of the field?

Let x be the number of truffles.

3/13 of x = 39

3x/13 = 39

x = 39 ⋅(13/3)

x = 169

Remaining number of truffles = 169-39

= 130

Example 4 :

Last week we picked 1/ 3 of our grapes and this week we picked 1/ 4 of them. So far we have picked 3682 kg of grapes. What is the total weight of grapes we expect to pick?

Let x be total number of grapes.

Number of grapes picked last week = 1/3 of x

= x/3

Number of grapes picked this week = (1/4) of x

= x/4

(x/3) + (x/4) = 3682

7x/12 = 3682

x = 3682 ⋅ (12/7)

x = 6312 kg

So, total weight of grapes is 6312 kg.

Example 5 :

Annika pays 2/25 of her weekly income into a retirement fund. If she pays $42 into the retirement fund, what is her :

a) weekly income

b) annual income?

a) Let x be the Annika's weekly income.

2/25 of x = 42

2x/25 = 42

x = 42(25/2)

x = 525

Her weekly income is $525.

b) 52 weeks = 1 year

Annual income = 52(525)

= $27300

Example 6 :

Jamil spent 1/4 of his weekly salary on rent, 1/5 on food, and 1/6 on clothing and entertainment. The remaining money was banked.

a) What fraction of Jamil’s money was banked?

b) If he banked $138:00, what is his weekly salary?

c) How much did Jamil spend on food?

Let x be his salary.

Money spent for rent = 1/4 of x

Money spent for food = 1/5 of x

Money spent for clothing = 1/6 of x

Part of money banked = x - [(x/4)+(x/5)+(x/6)]

= x - (37x/60)

= 23x/60

So, the fraction of money banked is 23/60.

(b) 23x/60 = 138

x = 138(60/23)

x = 360

His salary is $360.

= 360/5

Example 7 :

In autumn a tree starts to shed its leaves. 2/5 of the leaves fall off in the first week, 1/2 of those remaining fall off in the second week, and 2/3 of those remaining fall off in the third week. 85 leaves now remain.

a) What fraction of leaves have fallen off at the end of:

(i) the second week (ii) the third week?

b) How many leaves did the tree have to start with?

Let x be the total number of leaves.

Number of leaves fall off in the first week = 2/5 of x

= 2x/5

Number of leaves fall off in the second week

= (1/2) of 3/5 of x

= 3x/10

Number of leaves fall off in the third week

= (2/3) of 3/10 of x

= x/5

(i) Fraction of leaves fall off at the end of the second week

= (2x/5) + (3x/10)

= 7x/10

So, the answer is 7/10.

(ii) Fraction of leaves fall off at the end of the third week

= (2x/5) + (3x/10) + (x/5)

= 9x/10

So, the answer is 9/10.

(ii) Total number of leaves initially :

9x/10 + 85 = x

x/10 = 85

x = 850

So, the total number of leaves is 850.

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Unitary Method (Types, Formula & Problems)
Unitary method is used to find the value of single unit and multiplying it with number of units for the necessary value. Learn how to solve problems of ratio and proportion using unitary method. ... In this case, the apples are the units, and the cost of the apples is the value. While solving a problem using the unitary method, it is important ...
Unitary Method
Unitary Method. Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit. It is a method that we use for most of the calculations in math. You will find this method useful while solving questions on ratio and proportion, algebra ...
Unitary Method
This video shows how to solve problems using the Unitary Method.Textbook Exercises: https://corbettmaths.com/2019/10/04/unitary-method-textbook-exercise/
Mastering Math Made Easy: How to Use the Unitary Method
The Unitary Method is a problem-solving technique commonly used in math. It involves using the relationships between different units of measurement to solve problems. For example, if you know that 1 meter equals 100 centimeters, you can use this relationship to convert between the two units. This is a simple example of the Method in action.
Mixed Problems Using Unitary Method
Solved examples of mixed problems using unitary method: 1. If 24 painters working for 7 hours a day, for painting a house in 16 days. How many painters are required working for 8 hours a day will finish painting the same house in 12 days? Solution: 24 painters working for 7 hours paint a house in 16 days.
Unitary Method: Meaning, Concepts with Solved Examples and Videos
In other words, the method by which we find out the value of one unit and further use it to find the value of multiple units is known as the unitary method. Let us understand the application of unitary method by an example: Suppose Ram buys a dozen (12) bananas for 36 Rs. The cost of 12 bananas = 36 Rs. The cost of 1 banana = 36÷12 = 3 Rs.
Unitary Method: Formula and Solved Examples
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple. Unitary method in Hindi is known as ऐकिक नियम.
Unitary method
Unitary method. In elementary algebra, the unitary method is a problem-solving technique taught to students as a method for solving word problems involving proportionality and units of measurement. It consists of first finding the value or proportional amount of a single unit, from the information given in the problem, and then multiplying the ...
Unitary Method
While solving a problem using the unitary method, it is important to recognize the units and values. For simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side. In the above problem, we know the amount of the number of apples and the value of the apples is unknown.
Unitary Method Textbook Exercise
Unitary Method Textbook Exercise - Corbettmaths. Welcome. Videos and Worksheets. Primary. 5-a-day.
Definition and Example Of Unitary Method Problems
The unitary method is a fundamental concept of Mathematics and makes it convenient to solve various sums. This method generally involves finding the value of a unit in the given terms, using which the value of the given quantity of units can be calculated. The following example will help you understand the terms 'unit' and 'value'.
Unitary Method Worksheet
Section 1 of the unitary method worksheet contains 24 skills-based unitary method questions, in 3 groups to support differentiation. Section 2 contains 5 applied unitary method questions with a mix of word problems and deeper problem solving questions. Section 3 contains 4 foundation and higher level GCSE exam style unitary method questions.
Unitary Method
The method to find out the value of one unit (item) which in turn used to find the value of required number of units is called an unitary method. Working Rules for Solving Problem Using Unitary Method: Step I: Express the given data in a Mathematical statement such that the quantity which is to be found comes at the end of the statement.
Unitary Method Questions With Solutions
Following are some questions on unitary method of direct variation type. Question 1: If the price of 5 kg potato is ₹ 150. Find the value of 24kg potato. Solution: Price of 5 kg potato = ₹ 150. Price of 1kg potato = ₹ 150/5 = ₹ 30. Price of 24 kg potato = 24 × 30 = ₹ 720. Question 2: A pack of 120 soaps is ₹ 540.
Rate problems (practice)
Solving unit rate problem. Video 2 minutes 1 second. 2:01. Solving unit price problem. Report a problem. ... Lesson 3: Unitary method. Intro to rates. Solving unit rate problem. Solving unit price problem. Unit rates. Rate problems. Comparing rates example. Comparing rates. Math > Class 9 > Ratio and proportion >
Worksheet on Word Problems on Unitary Method
Answers for the worksheet on word problems on unitary method of direct variation and inverse variation are given below to check the exact answers of the above problems. Answers: 1. 16 farmers. 2. $928. 3. 21 5/7 kg, 35 books. 4. 105 words. 5. $2875. 6. 5 hours. 7. 25.
Unitary Method: Types and Examples
Unitary Method is a fundamental approach in mathematics used to solve problems related to finding the value of a single unit and then the value of multiple units. It's based on the concept of proportionality , which means if one quantity increases or decreases, the other does so in a direct or inverse proportion.
Unitary Method: Know Definition, Types, Steps to Use, Examples
Unitary Method is a technique for solving a problem by first finding the value of a unit quantity, and then finding the required value by multiplying the unit rate quantity value with it. We use this method to calculate the missing value. ... Unitary Method Solved Examples. Problem 1: The cost of 2 notebooks is Rs. 90. Calculate the cost of 10 ...
What is Unitary Method? Worksheets and Problems of Unitary Method (PDF
The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result. The unitary method is widely used in mathematics to solve word problems of various kinds like algebra, ratio, proportions, geometry, etc. The word unitary itself ...
UNITARY METHOD WITH FRACTIONS
UNITARY METHOD WITH FRACTIONS. If 4/7 of an amount of money is $480, then 1/7 of the amount is. = $480 ÷ 4. = $120. Thus 6/7 of the amount = 6x $120 = $720. and 7/7 is the whole amount which is 7 x $120 = $840. So, given the value of a number of parts of a quantity we can find one part of the quantity and then the whole quantity or another ...
Maths
Hello, BodhaGuru Learning proudly presents an animated video in English which explains the use of unitary method in an elaborate way. Learn to use unitary me...
Solving Problems with the Unitary Method
To find the cost of 11, we must use the unitary method. Find the cost of 1 eraser first and then find the cost of 11. 6 erasers = £0.60. ÷ 6. 1 eraser = £0.10. × 11. 11 erasers = £1.10. Twinkl Twinkl Go Secondary Maths. This interactive resource challenges students to solve direct proportion worded questions using the unitary method by ...
Discover the Power of Unitary Method in Problem Solving
The unitary method is a technique for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.. It takes 3 hours to cook an 8-pound turkey. How long would it take to cook a turkey that is 14 pounds? A problem can be solved using the unitary method by first determining the value of a single unit, and then ...

Unitary Method

What is Unitary Method?

Steps to Use Unitary Method

Types of Unitary Method

Direct Variation in Unitary Method

Indirect Variation in Unitary Method

Unitary Method in Ratio and Proportion

Real-Life Applications of Unitary Method

Topics Related to Unitary Method

Unitary Method Word Problems

Practice Questions on Unitary Method

What is the Unitary Method for Percentage?

What is the Formula for Unitary Method?

What is the Unitary Ratio?

What are the Types of Unitary Method?

What is Unitary Method in Ratio and Proportion?

Mastering Math Made Easy: How to Use the Unitary Method

Introduction

Understanding the Method: Definition and Examples

Applications in Real-Life Situations

Advantages of Using the Unitary Method in Math Problem Solving

Step-by-Step Guide to Using the Unitary Method

Common Mistakes to Avoid

Practice Problems

Additional Resources for Learning and Practicing the Method

Tips for Applying the Method in Various Math Concepts

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Table of Contents

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The Three States of Matter: Solids, Liquids, and Gases

Types of Motion: Introduction, Parameters, Examples

Understanding Frequency Polygon: Detailed Explanation

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Air Pollution: Know the Causes, Effects & More

Sexual Reproduction in Flowering Plants

Integers Introduction: Check Detailed Explanation

Unitary Method: Formula and Solved Examples

What is Unitary Method?

Ratio Proportion and Unitary Method

Types of Unitary Method

Direct Variation

Indirect Variation

Unitary Method for Time and Work

Unitary Method Questions

Worksheet on Word Problems on Unitary Method

Real-Life Applications of Unitary Method

Solved Examples – Unitary Method Formula

FAQs on Unitary Method

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