Two pipes X and Z can fill a tank in 36 hours and 48 hours respectively, while pipe Y can drain the tank in 72 hours. If pipes X and Z are opened together for 10 hours and then Z is closed and Y is opened, how long will it take to completely fill the tank?

ATQ,

Let capacity of the tank = 288 litres (LCM of 36, 48, and 72)

Water filled by pipe X in 1 hour = 288 / 36 = 8 litres

Water filled by pipe Z in 1 hour = 288 / 48 = 6 litres

Water drained by pipe Y in 1 hour = 288 / 72 = 4 litres

In first 10 hours, X and Z together fill:

= 10 × (8 + 6) = 10 × 14 = 140 litres

Remaining volume to be filled = 288 – 140 = 148 litres

Now only pipes X and Y are open, so effective rate = 8 – 4 = 4 litres/hour

Time to fill remaining tank = 148 / 4 = 37 hours

Total time taken = 10 + 37 = 47 hours