Inverse Proportion:
Suppose that 20 men build a house in 6days. If men are increased to 30 then they take 4days to build the same house. If men become 40, they take 2days to build the house.
i.e.
It can be seen that as the no. of men is increased, the time taken to build the house is decreased in the same ratio.
In other words,
If increased in one quantity causes decrease in other quantity or decrease in one 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
Shows each product is constant or same.
Therefore, if we are dealing with quantities, which are related inversely, the 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 by 7 pipes?
Solution:
By the principle of inverse proportion, we have
4 x 70 = 7 x
= 40 minutes
Example:
Thirtyfive workers can build a house in 16days. How many days will 28 workers working at the same rate take to build the same house?
Solution:
By the principle of inverse proportion, we have
28 x = 35 x 16
= 20 days
Example:
Imran brought 40 toys each cost Rs.14. How many toys Imran can buy at Rs.8 each from the same amount?
Solution:
By the principle of inverse proportion, we have
14 x 40 = 8 x
= 70 toys
