Two pipes A and B can fill a cistern in 12 minutes and 16 minutes respectively. If both the pipes are opened together, then after how much time B should be closed so that the tank is full in 9 minutes ?

A. 3 min and 30 sec.   
B. 4 min and 30 sec.
C. 4 min.   
D. 4 min 77 sec.
Answer:     C

Explanation:     

A tank can be filled by a tap in 20 minutes and by another tap in 6O minutes Let B be closed after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (9 — x) min, = 1
x[(1/12) + (1/16)] + (9 - x)(1/12) = 1 or (7x/48) + (9-x)/12 = 1
or7x + 36 — 4x = 48 or x=4.
So, B must be closed after 4 minutes.