Question

a pump can fill a tank in 4 hours,but due to leak ,the tank now gets filled in 5 hours.How long will it take the leakage to empty the tank when it is full?​

Answer 1

Given,

A Pump can fill the tank in 4 hours

Tank leaks so, after leakage tank can be filled in 5 hours

Work done by the pump = 1/4

Let the time taken to empty the tank be x

Work done by leakage = 1/x

Both are worked together,

$\frac{1}{4} - \frac{1}{x} = \frac{1}{5}$

Here I used negative sign before 1/x because it indicates leakage.

$- \frac{1}{x} = \frac{1}{5} - \frac{1}{4}$

$- \frac{1}{x} = \frac{1 \times 4}{5 \times 4} - \frac{1 \times 5}{4 \times 5}$

$- \frac{1}{x} = \frac{4}{20} - \frac{5}{20}$

$- \frac{1}{x} = - \frac{1}{20}$

$- x = - 20$

$x = - ( - 20)$

$x = 20$

It takes 20 hours to empty tank when it is full.