# Class-7 Unitary Method

Introduction to 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

## Answer Sheet

**Unitary-Method-Answer**Download the pdf

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