Class-7 Unitary Method

Introduction to Unitary Method

A method, in which the value of one article is first obtained to find out the value of any required articles, is known as unitary method.

Value of required number of articles = (Value of one article) × (Required number of articles)

Type of Variations

Direct Variation
Inverse Variation

Direct Variation

Increase / decrease in one quantity causes increase / decrease in other quantity respectively. From our day-to-day life let's discuss some examples.

With more money one can buy more articles.
With more speed one can travel more distance.
With a smaller number of men / women, less work can be done.

Let's see some mathematical examples to understand unitary method's direct variation.

Example 1. If 6 pen cost Rs. 72, then what will be the cost of 25 such pens?

Solution. Cost of 6 pen = Rs. 72

Cost of 1 pen = ⁷²⁄₆ = Rs. 12

Cost of 25 pens = 12 × 25

= Rs. 300

Hence, cost of 25 pens is equal to Rs. 300

Example 2. A motor bike can go 600 km in 15 liters of fuel. How far it can go with 50 liters of fuel?

Solution. With 15 liters of fuel a motor bike can go 600 km.

With 1 liter of fuel the motor bike can go = ⁶⁰⁰⁄₁₅ = 40 km

With 50 liters of fuel, it can go = 40 × 50

= 2000 km

Hence, with 50 liters of fuel motor bike can go 2000 km.

Example 3. Mr. John earns Rs. 6300 for working in 7 days. How much he will earn in 30 days?

Solution. Mr. John earns Rs. 6300 for working in 7 days.

In 1 day Mr. John earns = ⁶³⁰⁰⁄₇

= Rs. 900

In 30 days Mr. John will earn = 900 × 30

= Rs. 27000

Hence, Mr. John will earn Rs. 27000 in 30 days.

Example 4. If 18 meters of cloth cost Rs. 2250. How many meters of it can be bought for Rs. 5000?

Solution. For Rs. 2250, cloth bought = 18 meters

For Rs. 1, cloth can be bought = ¹⁸⁄₂₂₅₀ m

For Rs. 5000, cloth can be bought = ¹⁸⁄₂₂₅₀ × 5000

= 40 m

Hence, the length of the cloth bought for Rs. 5000 is 40 m.

Example 5. If 7.5 liters of milk cost Rs. 50, then how much milk will cost Rs. 2500?

Solution. For Rs. 50, milk quantity can be bought = ^7.5⁄₅₀ liter

For Rs. 2500, amount of milk can be bought = ^7.5⁄₅₀ × 2500

= 375 liters

Hence, the amount of milk can be bought for Rs. 2500 is 375 liters.

Example 6. If 15 men can weave 90 meters of cloth in a day, how many meters of cloth can be woven by 7 men in a day?

Solution. 15 men can weave 90 meters of cloth in a day.

1 man can weave = ⁹⁰⁄₁₅ = 6 meters

7 men can weave = 6 × 7 = 42 meters

Hence, 7 men can weave 42 meters of cloth in a day.

Inverse Variation

If we increase one quantity, then it will decrease other and if we decrease one quantity, then it will increase other. Let's consider some day-to-day examples.

With more men less days will be required to complete the work.
With high speed less time will be required to cover same distance.

Let's see some examples to understand it better.

Example 1. 20 men can do a work in 5 days. How many men will do it in 2 days?

Solution. In 5 days, work can be completed by 20 men.

In 1 day, the entire work can be completed by = 20 × 5 = 100 men

In 2 days, the entire work can be completed by = ¹⁰⁰⁄₂ = 50 men

Hence, 50 men can complete the work in 2 days.

Example 2. With a speed of 90 km/h, it takes 4 hours to cover distance from Kolkata to Bhubaneswar. What should be the speed if the same journey is to be completed by 3 hours.

Solution. To cover the distance between Kolkata to Bhubaneswar in 4 hours, speed required = 90 km/h

To cover the same distance in 1 hour, speed required = 90 × 4 = 360 km/h

To cover the same distance in 3 hours, speed required = ³⁶⁰⁄₃ = 120 km/h

Hence, to cover the distance between Kolkata to Bhubaneswar in 3 hours one would need 120 km/h.

Unitary Method Worksheet

Unitary Method Worksheet - 1

Unitary Method Worksheet - 2

Answer Sheet

Unitary-Method-AnswerDownload the pdf

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