Page 139 - Maths Skills - 8

Direct and Inverse Proportions 137

Example 2: If 40 men can finish a piece of work in 30 days, how many days will 20 men take to do it?
Solution: Let 20 men take x days to complete it. We may put the given data in a table as under.

Number of men (p) 40 20

Number of days (q) 30 x

Clearly, the lesser the number of men, the more will be the number of Alternative Approach
days to finish the work. men days
So, it is a case of inverse (indirect) Proportion. 40 30

The ratio of the number of men = inverse ratio of the number of days. 20 x

So, 40 : 20 = x : 30 Here, 40 = x
20 30
40 x
⇒ 20 = 30 or x 40 30
20
40 × 30 or x = 60 days
⇒ x = = 60
20

Example 3: Working 5 hours a day, Suresh can type a book in 27 days. How many hours a day should he work
to finish the same book in 9 days?

Solution: Suppose working x hours a day he can finish it in 9 days. The given data may be put in a table as
follows.

Hours (p) 5 x
Number of days (q) 27 9

Clearly, lesser the number of days to finish a book, the greater the Alternative Approach
number of hours required. So, it is a case of inverse proportion. men days
We know that, ratio of hours = Inverse ratio of number of days i.e., 27 5
5 : x = 9 : 27 9 x
5 9 Here, x = 27
⇒ x = 27 5 9

⇒ x = 5 × 27 = 15 or 9x = 5 × 27

9 or x 527
\ Working 15 hours a day, Suresh can finish the book in 9 days. 9
= 15 hours

Exercise 9.2

1. If p and q vary inversely, find the constant Proportion and complete the table.

(i) p 9 3 – 4 – (ii) p 12 3 – 15 –
36
–
q 8 – 6 q 10 – 20 – 5
2. In which of the following cases do the two quantities p and q vary inversely.
(i) p 8 4 2 16 3 (ii) p 2 4 1 8 6
6
32
q 12 24 48 q 9 18 4.5 36 37