A pipe can fill a water tank in 36 minutes, and another can fill it in 48 minutes, but a third pipe can empty it in 18 minutes. The first two pipes are kept open for 16 minutes at the beginning, and then the third pipe is also opened. How long does it take to empty the tank?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 112 minutes .
Pipe1 fills in 36 min → rate = 1/36 tank per min
Pipe2 fills in 48 min → rate = 1/48 tank per min
Pipe3 empties in 18 min → rate = −1/18 tank per min
First 16 min, only Pipe1 and Pipe2 open: (1/36 + 1/48) × 16 = 7/9 tank filled
Remaining water = 1 − 7/9 = 2/9 tank
All three pipes open: net rate = 1/36 + 1/48 − 1/18 = −1/144 tank per min
Time to empty remaining water = (7/9) ÷ (1/144) = 112 min