Page 99 - ICSE Math 7

3. Form all possible proportions using the following numbers.
1 22 4 3
, ,
(a) 5, 2, 4, 10 (b) 0.4, 1.4, 0.7, 0.2 (c) 2 15 5 11
,
4. Which of the following quantities are in continued proportion?
(a) 3, 9, 27 (b) 5 m, 10 m, 30 m (c) ` 7, ` 9, ` 63 (d) 6, 5, 25

5. Find the mean proportional between the following.
1
3
(a) 3 and 12 (b) 9 and 36 (c) 4.5 and 0.5 (d) and 49
3
6. Find the third proportional to the following.
1
2
3
(a) ` 5, ` 25 (b) 0.4, 0.6 (c) m, m (d) : 1
3 8 5 4
Unitary Method
A unit is defined as a single object or person. In unitary method, the Try These
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, 1. The cost of 18 m cloth is
` 1,260. What will be the cost
and multiply to get more. For example, if the price of 5 books is given of 7 m cloth?
as ` 335 and we wish to find the price of 7 books, we divide to get and 2. The cost of 15 articles is
335 ` 2,175, find the cost of 12
the price of 1 book which is ` = ` 67. So, the price of 7 books is such articles.
5
` 67 × 7 = ` 469.

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. We use division to find
the value of a unit quantity 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. We use multiplication to find the value of a unit quantity in inverse
variation.
Example 18: A man earns ` 15,750 in 15 days. How much will he earn in 28 days?

Solution: Money earned and the number of days are in direct
variation. Maths Info

Earning in 15 days = ` 15,750 The statement is written in such
15,750 a way that the required quantity
∴ Earning in a day = ` = ` 1,050 is at the end of the statement.
15
∴ Earning in 28 days = ` 1,050 × 28 = ` 29,400.

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