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

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