Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed so that the tank is full in 9 min?

Correct Answer: 20 min

Part filled by A in 1 min = 1/24

Part filled by B in 1 min = 1/32

Let B is closed after x min. Then, [Part filled by (A + B) in x min] + [Part filled by A in (9-x) min] = 1

Therefore,

x(1/24+1/32)+(9−x)×1/24=1

=> x(4+3/96)+(9−x)/24=1

=> 7x/96+(9−x)/24=1

=> 7/x+4(9−x)/96=1

=> 7/x+4(9−x)=96

=> 7x+36-4x=96

=> 7x – 4x = 96 – 36

= 3x = 60 => x = 60/3 = 20

Hence, B must be closed after 20 min.