Page 115 - ICSE Math 6

2. Determine x if 72 : 112 : : x : 28.
3. The numbers 5, 21, 25 and x are in proportion. Find x.

4. In a proportion, the first, second and fourth terms are 3, 5 and 25 respectively. Find the third term.
5. In a proportion, the second, third and fourth terms are 7, 35 and 49 respectively. Find the first
term.

Unitary Method

In unitary method, the value of a unit quantity is obtained first to find the value of the required quantity.
The basic principle of unitary method is to divide to get less, and multiply to get more. For example,
if the price of 5 books is given as ` 335 and we wish to find the price of 7 books, we divide to get the
335
price of 1 book which is ` = ` 67. So, the price of 7 books is ` 67 × 7 = ` 469.
5
Variation

Variation means change in one quantity with respect to the other quantity. While using unitary method,
we will come across two types of variations:
(a) Direct variation (b) Inverse variation

Direct variation
Two quantities are said to be in direct variation if an increase or decrease in one quantity causes a
corresponding increase or decrease in the other quantity. For example, if 5 pencils can be bought with
` 20, then 10 pencils can be bought with ` 40. Thus, more is the amount of money, more is the number
of pencils. So, number of pencils and amount of money are in direct variation.

Inverse variation
Two quantities are said to be in inverse variation if an increase or decrease in one quantity causes a
corresponding decrease or increase in the other quantity. For example, if 5 men can complete a work
in 8 days, then 1 man will complete the same work in 5 × 8 = 40 days. Thus, lesser the number of
men to complete the work, more is the number of days required. So, number of men and number of
days are in inverse variation.

Example 12: If 14 identical bags of wheat weigh 126 kg, then how many such bags will weigh
198 kg?

Solution: Number of bags and weight of bags are in direct variation.
Weight is 126 kg when number of bags = 14
14 1
\ Weight is 1 kg when number of bags = =
126 9
1
\ Weight is 198 kg when number of bags = × 198 = 22
9
Example 13: If 600 apples can be packed into 25 identical cartons, then into how many such cartons
768 apples can be packed?

Solution: 600 apples can be packed into = 25 cartons
25
1 apple can be packed into = carton
600
25
768 apples can be packed into = × 768 = 32 cartons
600

99