Page 87 - Maths Skills - 7

Comparing Quantities 85

UNITARY METHOD

The method of finding the value of one unit from the value of the given numbers of items and the using it to find
the value of required number of items is called the unitary method.
For example; if the cost of 5 pens is ` 20, what will be the cost of 18 pens?
Cost of 5 pens = ` 20
Cost of 1 pen = ` 20 ÷ 5 = ` 4

Cost of 18 pens = ` 4 × 18 = ` 72
Here we have found the value of 1 pen first and then the value/cost of 18 pens. We have observed that if the
number of pens increases, the cost also increases. Similarly, when the quantity of pens decreases, the cost also
decreases. This sort of relation is called direct proportion.
Let’s learn through examples:

Let’s Attempt

Example 1: Rahul drives his car and travels 10 km 800 m in 12 minutes. What is the distance covered by him
in 1 hour?
Solution: Distance covered by Rahul in 12 minutes = 10 km 800 m [Q 1 km = 1000 m]

= 10000 + 800 m = 10800 m
Distance covered in 1 minute = (10800 ÷ 12) m

Distance covered in 1 hour (1 hour = 60 min.) = 10800 × 60 = 54000 m = 54 km
12
Example 2: Mrs. Arya earns ` 7500 for 15 days of work. How much will she earn if she works for 28 days?
Solution: Amount earned in 15 days = ` 7500

Amount earned in 1 day = ` 7500
15

Amount earned in 28 days = ` 7500 × 28 = ` 14,000.
15

Exercise 5.2

1. A printing machine can print 150 sheets for every 3 minutes. Find:
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(i) The time taken to print 3000 sheets. (ii) How many sheets can be printed in 1 hr?
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2. The cost of 17 metres of cloth is ` 1028.50. Find the cost of 80 metres of cloth.

3. Seema travels 73 km in 57 minutes. How many minutes will she take to travel 438 km?
4. 10 packets of tea leaves weigh 35 kg. What will be the weight of 53 such packets?

5. A journey of 500 km is covered by car using 20 litres of petrol. How much petrol will be used for a
journey of 750 km? What will be the distance that the car can travel with 27 litres of petrol?
6. An electric pole 5 m high gives a shadow 7.5 m long. At the same time a glass building has a shadow
97.5 m long. What is the height of the glass building?
7. In a mall, car parking charges are ` 10 for the first hour and ` 5 for every extra half an hour or part
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thereof. How much is the parking fee for 2 hrs?
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