Unitary Method: Steps, Types of Unitary Method, Solved Examples

Unitary method is process of finding value of single unit by using value of multiple units and then finding value of multiple units using value of single units. This method is mostly used in ratio and proportion concept. Unitary Method has two variations, direct variation and indirect variation. Direct variation is inverse to indirect variation. Unitary method is used to determine price of a good, profit or loss in business, calculating percentage, etc.

Key Terms: Unitary Method, Ratio, Proportion, Single Units, Multiple Units, Direct Variation, Indirect Variation

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Introduction to Unitary Method

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Procedure of finding value of single unit by using value of multiple units and then finding value of multiple units using value of single units is referred to as Unitary Method. Recognizing values and units is important while using unitary method to solve a problem.

For example: If 3 pencils cost 9 rupees, how much will 10 pencils cost? We can find the answer by using unitary method. One pencil will cost 3 rupees so 10 pencils will cost 30 rupees.

10 Apples = Rs 100

1 Apple = 100/10 = Rs 10

6 Apples = 10 x 6 = Rs 60

Unitary Method

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Steps to Use Unitary Method

Unitary method has two steps. It includes using division and multiplication.

Let us take an example for better understanding. Suppose 5 notebooks cost 150 rupees. How much will 7 notebooks cost?

Let us first note the information we have. We know that 5 notebooks cost 150 rupees.

Step 1: First, we have to find cost of one notebook. We can do that by dividing the total cost of 5 notebooks with total number of notebooks.

If 5 notebooks cost 150 rupees, one notebook = 150/5 = 30 rupees

Now we know that one notebook costs 30 rupees.

Step 2: We need to find cost of 7 notebooks.

If one notebook costs 30 rupees, 7 notebooks = 30 x 7 = 210 rupees

So, 7 notebooks cost 210 rupees.

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Types of Unitary Method

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There are 2 variations of unitary method: Direct Variation and Indirect Variation.

Direct Variation

When increase or decrease in one quantity leads to increase or decrease (respectively) in another quantity, it is direct variation. For example: if there is an increase in quantity of goods, there will be an increase in price. Another example: the amount of work done by multiple men will be more than amount of work done by one man. So, if we decrease the number of men, work done also decreases.

Indirect Variation

When there in an increase in value of one quantity, the value of another quantity decreases. When there is a decrease in value of one quantity, the value of another quantity increases. This is indirect variation. It is basically the inverse of direct variation. For instance, when we increase the speed of the vehicle, we can cover the distance in less time. So increase in speed leads to decrease in time.

Also Read: Natural Numbers and Whole Numbers Addition Subtraction and Division

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Uses of Unitary Method

Unitary method has many practical applications in different areas ranging from price, distance, speed, time etc.

Some of the most common applications of unitary method are:

• Profit and loss in business is determined using unitary method.
• Price of a good can be evaluated using this method.
• It helps in finding the number of people needed to finish a given amount of work
• Time taken to cover a specific distance in a specific time can be determined using unitary method.
• Percentage of a quantity can be calculated

Use of Unitary Method in Ratio and Proportion

Unitary method is also used to find the ratio of one quantity in relation to another.

For example: Income of Rakesh is 12000 per month and yearly income of Mahesh is 191520. They spend a total of 9960 every month; find the ratio of their savings using the unitary method.

Savings of Rakesh per month = 12000 – 9960 = 2040 Rupees

Yearly income of Mahesh = 191520 Rupees

Monthly income of Mahesh = 191520 / 12 = 15960 Rupees

Savings of Mahesh = 15960 – 9960 = 6000 Rupees

So the ratio of savings of Rakesh and Mahesh is 2040:6000 = 17:50

Also Read: 

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Things to Remember

• Unitary method is the process of finding the value of single unit by using value of multiple units and then finding the value of multiple units using value of single units.
• There are 2 variations of unitary method: Direct Variation and Indirect Variation.
• When increase or decrease in one quantity leads to increase or decrease (respectively) in another quantity, it is direct variation.
• When there in an increase in value of one quantity, the value of another quantity decreases. When there is a decrease in value of one quantity, the value of another quantity increases. This is indirect variation.
• Unitary method has many practical applications in different areas ranging from price, distance, speed, time etc.

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