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Concept of Unitary Method

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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.

notes

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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