Two pipes A and B can separately fill a cistern in 24 and 32 minutes respectively. They started to fill a cistern together, but B is turned off after few minutes and A fills the rest of the cistern. If total time taken is 18 minutes, after how many minutes is tap B turned off?

Question

kira_yamato · Answer

Let the volume of cistern be V and time when B turned off be t min
For every minute before t, the cistern is filled up at rate of (V/24 + V/32)
For every minute from t, the cistern is filled up at rate of V/24
t(V/24 + V/32) + V(18-t)/24 = V
Solve for t (see attached)