Question

A water tank is 3/5th full. Pipe a can fill a tank in 8 minutes while pipe b can empty it in 5 minutes. If both the pipes are open, how long will it take to empty/fill the tank completely?

Answer 1

Let the volume of the tank be x.

The volume filled by pipe a in 1 min is x/8.
The volume emptied by pipe b in 1 min is x/5.

Since the emptying is happening faster than filling the tank becomes empty.

Since the filling and emptying happening simultaneously , the net effect is
x/5 - x/8 = 3x/40 lts^3/min

Now the tank is 3/5th full, the time required to empty this is :

3x/40lts^3 = 1 min
3/5th of x = ymins

y * 3x/40 = (3/5)*x

Simplifying :

y = 8 mins