UNITARY METHOD
Unitary method is a way of carrying out calculations to find the value.
If the cost of one object is given, you can find the cost of many objects by multiplying the cost of one object with the number of objects..
EXAMPLE:1
Cost of 1 book is 20. What is the cost of 10 such books?
Solution: Cost of 1 book = Rs.20
Cost of 10 books = 20 x 10 =RS.200.
If you are given the cost of several objects, you can find the cost of one object by dividing the cost of several objects by the number of objects.
EXAMPLE 2:
Cost of 5 pens is 125. What is the cost of 1 pen?
Solution:
Cost of 5 pens =Rs. 125
Cost of 1 pen = Rs.125÷5
= RS. 25.
EXAMPLE: 3. Suppose, a car travels 90 kilometres in 3 hours. Calculate the speed of the car.
Calculating the speed of the car means we have to find the average distance covered by the car in 1 hour.
Distance travelled by the car in 3 hours =90 kilometres.
Distance travelled by the car in 1 hour = 90÷3 kilometres
= 30 kilometres.
Therefore, speed of the car is 30 kilometres per hour.
EXAMPLE 4. A work is completed by 10 men in 50 days. How long will 25 men take to complete the work?
Total work is completed by 10 men in 50 days.
Total work is completed by 1 man in 50 x 10 days = 500 days
(less number of men will take more days to complete the work).
Total work will be completed by 25 men in 500÷25 days = 20 days
(increase in the number of men will decrease the number of days needed to complete the work).
Therefore, the total work will be completed in 20 days by 25 men.
We use the unitary method to solve problems on measurement as well. First we find the length, capacit weight, time and then we find the required value.
EXAMPLE:5. A car can be driven 120 km on 8L of petrol. How may kilometers can it be driven on 30 L of petrol?
Solution:
Since 8L of petrol is needed to drive 120 km.
So, distance that can be driven in 1 Lof petrol
= 120 ÷ 8 =15 km.
1 Lof petrol can help us drive the car for 15 km
30 L of petrol can help us drive the car for 15 km x 30 = 450 km.
Exercise 14.1
1. 10 kg of rice costs 290
1 kg of rice costs= ......
28 kg of rice costs=
2. 15kg sugar costs =Rs.510
1kg of sugar costs =
5kg of sugar costs
3 12 dozen bananas cost Rs 216
1 dozen bananas cost=.
22 dozen bananas cost=
4. 15 oil tankers can carry 45000 L of diesel:
1 oil tanker can carry =
40 oil tanker can carry=
5. 1 tailor can make 5 large-size shirt from 10 m cloth:
1 large-size shirt can be made from cloth =
25 large-size shirt can be made from cloth=
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