Page 185 - Maths Class 06

10. Find the mean propor tion of 9 and 4.

11. A tin of refined oil is 8 cm high and can contain 352 l of oil. The manu fac turer increases the height
of the tin to 12.5 cm. How many litres can the new tin hold?

12. The first three terms of a proportion are 15, 20, 30. Find the fourth term.
13. Find the second term of a propor tion whose 1st, 3rd and 4th terms are 42, 70 and 35 respec tively.
14. The length and breadth of a rect an gle are in the ratio 6 : 3. If its length is 80 cm, find its breadth.
15. The map of a rect an gu lar field is drawn on a scale 1 : 90. If the actual length of the field is 270 m,
what will it be on the map?

Unitary Method

Consider the following example:
The cost of two tennis balls is ` 100. What would be the cost of three balls.

To solve the above question, we first need to find the value of one ball. Then that value can be used to
determine the value of any number of balls.

This method of calculation is called Unitary method that basically involves two steps:
(i) Calculating the cost of one unit

(ii) Finding the cost of the required number of units.
¸ ´
Given units ¾® One unit ¾® Required units

EXAMPLE 1. A truck travels 350 km in 7 litres of diesel. How much distance will it cover in 2.5 litres of
diesel?
SOLUTION : In 7 litres of diesel, truck can travel 350 km.
350
Therefore, in 1 litre of diesel, truck travels = = 50 km
7
Therefore, in 2.5 litres, truck travels = 2.5 ´ 50 = 125 km.

Thus, the truck can travel 125 km in 2.5 litres of diesel.
EX AM PLE 2. The weight of 15 scoot ers is 3375 kg. How many scoot ers can be loaded on a truck whose
ca pac ity of car ry ing load is 4500 kg?
SO LU TION : The num ber of scoot ers in 3375 kg = 15
15
\ The number of scooters in 1 kg =
3375
15 ´ 4500
\ The number of scooters in 4500 kg = = 20
3375
\ 20 scooters can be loaded on the truck.

Alternative Method
We can solve these example by an alternative method called a pro por tion method.
If two quantities are related to each other in such a way that when one increase or decreases there is a
corresponding increase or decrease in the other quantity such that the ratio of the two remains the same,
then those two quantities are said to be in direct proportion.

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