# Inverse Proportion

Suppose that 20 men build a house in 6 days. If the number of men is increased to 30 then they take 4 days to build the same house. If the number of men becomes 40, they take 2 days to build the house; i.e.

It can be seen that as the number of men is increased, the time taken to build the house is decreased by the same ratio.

In other words,

**if an increase in one quantity causes a decrease in another quantity, or a decrease in one quantity causes an increase in another quantity, then we say that both quantities are inversely related.**

More explicitly, if two quantities and are in inverse proportion, then their product will be constant.

i.e. where = constant

In the above example, we see that

20 x 6 = 120

30 x 4 = 120

40 x 3 = 120

This shows that each product is constant or the same.

Therefore, if we are dealing with quantities which are related inversely, then we can use the following rule:

20 x 6 = 30 x 4

In general,

**Example:**

Four pipes can fill a tank in 70 minutes. How long will it take to fill the tank with 7 pipes?

**Solution:**

By the principle of inverse proportion, we have

4 x 70 = 7 x

= 40 minutes

**Example:**

Thirty-five 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:**

By the principle of inverse proportion, we have

28 x = 35 x 16

= 20 days