Lesson 11, Topic 3
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# Inverse Proportion

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

### Example 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.

$$\scriptsize x \: \times \: 28 = 35 \: \times \: 16$$

28    =   35 x 16

Divide both sides by 28

$$\frac{28x}{28} = \frac{35 \; \times \; 16}{28}$$

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

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

$$\scriptsize x = 5 \; \times \; 4$$

$$\scriptsize x = 20 \; days$$

### Example 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

y   x  1  =   20 x 10

y  =  200 days

It will take 1 man 200 days

b. 4 men

4 x b =  20 x 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:

1.    If 2 eggs are needed to make 20 pancakes how many eggs are needed to make 100 pancakes?

2.    If 15 exercise books cost ₦45, what is the cost of

a.    1 similar exercise book
b.    125 similar exercise books

3.    In 5 hours, a car travelled 550km, How long will it take to travel

a.    1320km
b.    1540km

4.    25 men can eat 10 tubers of yam for breakfast. How many tubers of yam can 125 men eat?

5.    9 men can do a certain job in 12 days. How long will it take

a.    6 men
b.    3 men
c.    y men.  Assuming they work at the same rate.

6.    12 women can harvest a cassava farm in 20 days. How long will it take 5 women to do the same work? assuming that the women work at the same rate.

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