Two pipes A and B can fill a tank in 48 minutes and 66 minutes, respectively. If both the pipes are opened simultaneously, then after how many minutes should pipe B be closed so that the tank gets filled in 32 minutes?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 22.
Given that, Time taken by pipe A to fill the tank = 48 minutes
Time taken by pipe B to fill the tank = 66 minutes
Time taken by both to fill the tank = 32 minutes
Total work = Efficiency × Time
Let the total work to be done LCM(48, 66) be 528 units.
According to the given question,
Efficiency of pipe A = = 11 units/minute
Efficiency of pipe B = = 8 units/minute
Let pipe B be closed after x minutes.
⇒ (Efficiency of A + B)x + Efficency of A(32 - x) = 528
⇒ 19x + 11(32 - x) = 528
⇒ 19x + 352 - 11x = 528
⇒ 8x = 176
⇒ x = 22
Hence pipe B should be closed after 22 minutes.