There are two taps to fill a tank and a third to empty it. When the third tap is closed, the first two can fill the tank in 10 minutes and 12 minutes, respectively. If all three taps are opened, the tank is filled in 15 minutes. If the first two taps are closed, how long will the third tap take to empty a full tank?
A
7 min
B
9 min and 32 sec
C
8 min and 34 sec
D
6 min
Correct Option:
C
Explanation
The first two taps fill at 1/10 + 1/12 = 11/60 of the tank per minute. All three together fill at 1/15 = 4/60, so the third tap alone empties at 7/60 of the tank per minute. It therefore empties a full tank in 60/7 minutes, about 8 minutes 34 seconds.
