pipes and cistern

Question

Two taps t1 and t2 fill water at 12litres/min and 6 litres/min respectively.A leak pipe l can empty full tank in 10 min.If both taps and leak are opened tank can be filled in 15 min.

How much is capacity of tank?

1)96 litre

2)108litres

3)120 litres

4)cant be determined

Answer 1

p1+p1=18 litre/min

leak pipeworks = 1/10 per min

tank filled in 15min , totalworkratepermin =1/15

(inletwork - leakagework)=totalworkratepermin

inlet work rate=totalworkratepermin + leakage work =(1/15)+(1/10)=1/6

therefore, inlet pipe fill at the rate (1/6)per min.i.e tank is filled in 6 min

speed of both inlet given=18litrepermin

Capacity of tank=6*18=108 liters.