Inverse Proportion

What is Inverse Proportion?

Two quantities are in inverse proportion if one increases and the other decreases at the same rate.

Worked Example 11.3.1:

35 workers can build a house in 16 days. How many days will it take 28 workers working at the same rate to build the same house?

Solution

1. Let x represent the number of days it will take 28 works.

No of workers	No of days
35	16
28 (the number of workers decreased)	x (the number of days will increase)

\( \scriptsize x \: \times \: 28 = 35 \: \times \: 16 \)

28    =   35 × 16

divide both sides by 28

\( \frac{28x}{28} = \frac{35 \; \times \; 16}{28} \)

\( \scriptsize x = \normalsize \frac{35 \; \times \; 16}{28} \)

\( \scriptsize x = \normalsize \frac{5 \; \times \; 16}{4} \)

\( \scriptsize x = 5 \; \times \; 4 \)

\( \scriptsize x = 20 \; days\)

Worked Example 11.3.2:

20 men can do a certain job in 10 days. How long will it take

a. 1 man
b. 4 men
c. x men

Solution:

a. 1 man

No of men	No of days
20	10
1 (the number of men decreased)	y (the number of days will increase)

y   ×  1  =   20 × 10

y  =  200 days

It will take 1 man 200 days

b. 4 men

No of men	No of days
20	10
4 (the number of men decreased)	b (the number of days will increase)

4 × b =  20 × 10

4b  = 200

divide both sides by 4

\( \frac{4b}{4} = \frac{200}{4} \\ \scriptsize b = 50 \)

It will take 4 men 50 days 

c. x men

If it takes 1 man 200 days

It will take x men \( \frac{200}{x} \) days

Evaluation Questions: