# Concept of Unitary Method

## Definition

Unitary Method: The method in which first we find the value of one unit and then the value of the required number of units is known as Unitary Method.

# Unitary Method:

Consider the following situations:
1. Two friends Reshma and Seema went to the market to purchase notebooks. Reshma purchased 2 notebooks for Rs. 24. What is the price of one notebook?
Cost of 2 notebooks is Rs. 24.
Therefore, cost of 1 notebook = Rs. 24 ÷ 2 = Rs. 12.
Now, if you were asked to find the cost of 5 such notebooks. It would be = Rs. 12 × 5 = Rs. 60

2. A scooter requires 2 litres of petrol to cover 80 km. How many litres of petrol is required to cover 1 km?
We want to know how many litres are needed to travel 1 km.
For 80 km, petrol needed = 2 litres.
Therefore, to travel 1 km, petrol needed = 2/80 = 1/40 litres.
Now, if you are asked to find how many litres of petrol are required to cover 120 km?
Then petrol needed = 1/40 xx 120 litres = 3 litres.
• The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

• Find the cost of one article from that of many, by division. Then find the cost of many articles from that of one, by multiplication. This method of solving a problem is called the unitary method.

## Example

A motorbike travels 220 km in 5 litres of petrol. How much distance will it cover in 1.5 litres of petrol?

In 5 litres of petrol, motorbike can travel 220 km.

Therefore, in 1 litre of petrol, motorbike travels = 220/5 km.

Therefore, in 1.5 litres, motorbike travels

= 220/5 xx 1.5  "km" = 220/5 xx 15/10 km = 66 km.

Thus, the motorbike can travel 66 km in 1.5 litres of petrol.

## Example

If the cost of a dozen soaps is Rs. 153.60, what will be the cost of 15 such soaps?

We know that 1 dozen = 12
Since, cost of 12 soaps = Rs. 153.60

Therefore, cost of 1 soap = 153.60/12 = Rs. 12.80

Therefore, cost of 15 soaps = Rs. 12.80 × 15 = Rs. 192.

Thus, cost of 15 soaps is Rs. 192.

## Example

Cost of 105 envelopes is Rs. 350. How many envelopes can be purchased for Rs. 100?

In Rs. 350, the number of envelopes that can be purchased = 105.

Therefore, in Rs. 1, number of envelopes that can be purchased = 105/350

Therefore, in Rs. 100, the number of envelopes that can be purchased

= 105/350 × 100 = 30.

Thus, 30 envelopes can be purchased for Rs. 100.

## Example

A car travels 90 km in 2 1/2hours.
(a) How much time is required to cover 30 km with the same speed?
(b) Find the distance covered in 2 hours with the same speed.

(a) In this case, time is unknown and distance is known. Therefore, we proceed as follows:

2 1/2 "hours" = 5/2 "hours" = 5/2 × 60 "minutes" = 150 "minutes".

90 km is covered in 150 minutes.

Therefore, 1 km can be covered in (150)/(90) minutes.

Therefore, 30 km can be covered in (150)/(90) × 30 minutes i.e., 50 minutes.

Thus, 30 km can be covered in 50 minutes.

(b) In this case, distance is unknown and time is known. Therefore, we proceed as follows:

Distance covered in 2 1/2 "hours (i.e.," 5/2 hours ) = 90 km.

Therefore, distance covered in 1 hour = 90 ÷ 5/2 "km" = 90 × 2/5 = 36 km.

Therefore, distance covered in 2 hours = 36 × 2 = 72 km.

Thus, in 2 hours, the distance covered is 72 km.

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