Question

Two pipes can fill a tank in 30 min and 40 min respectively. Simultaneously when filling water it flows out entirely in 24 min. If the tank is filled by both pipes , how long will it take to fill the tank?

Answer 1

Let the volume of tank be 'V' in some units.
The time rate at which the pipes fill is $\frac{V}{30}$ and $\frac{V}{40}$.
Time rate at which the tank is emptied is $\frac{V}{25}$.
Time rate at which tank is filled is, $\frac{V}{30} + \frac{V}{40} - \frac{V}{24} = \frac{V}{60}$.
Hence, it takes 60 minutes or 1 hour to fill the tank.

Answer 2

Volume of tank = V litres

Filling rate of pipe 1  =  V / 30  litres/ minute
Filling rate of pipe 2 = V / 40  litres/min

Adding both,  Total filling rate =  7 * V / 120    litres/min

Suppose there is a leak, or there is an opening, through which water in the tank is emptied in 24 minutes.  So emptying rate of this = V / 24  litres/min

Then filling rate will be  7 * V / 120  - V / 24 = 2V/120 = V /60  litres/min

The time taken to fill the tank , while there is some water flowing out also,
               V / [V/60] = 60 minutes.