Question

Three pipes a b and c can fill a tank in 20,30and 40 minutes respectively.after 5 min a is closed and then after 6 min b is closed.at the moment a leak was developed which can empty the tank in 60 minutes.time taken to fill the tank?

Answer 1

Filling upto 5 min.=5*[(1/20)+(1/30)+(1/40)]=13/24
For next 6 min. only taps 'B' & 'C' are opened, so filling=6*[(1/30)+(1/40)]=7/20
Total filling upto first 11 min.=(13/24)+(7/20)=107/120 so remaining=13/120
As after this only tap 'C' and leakage @1/60 per min. are opened,
so its 1 min. filling rate= (1/40)-(1/60)=1/120
Time taken to fill remaining 13/120 tank= (13/120)/(1/120)= 13 min.
So total time taken to completely fill the tank= 5+6+13=24 min.