Two pipe  A and B c an fill a cistern in 32 minutes and 48 minutes respectively. Both the pipes are opened together for some time and then pipe B is turned off. What is the pipe B must be turned off so that the cistern gets filled in 24 minutes ?

12 min

The correct answer is option (1) : 12 min

Part of the tank filled by both the pipes in 1 min $=\frac{1}{32}+\frac{1}{48}=\frac{5}{96}$

Let pipe B be turned off after t min

$⇒t×\frac{5}{96}+(24-t)×\frac{1}{32}=1$

$5t+72-3t=96$

$2t=24$

$t = 12$

Hence, pipe B is turned off after 12 min.