Pipes A and B can fill an empty tank in 12 hours and 15 hours respectively, and pipe C can empty the full tank. The tank is empty and all three pipes are opened at the same time; the tank is then full in 10 hours. In how many hours can pipe C alone empty the full tank?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 hours
With all three open, the tank gains A's work + B's work − C's work in one hour. Take the capacity as the LCM of 12, 15 and 10, that is 60 units.
A fills \(\frac{60}{12}=5\) units and B fills \(\frac{60}{15}=4\) units in one hour
All three together gain \(\frac{60}{10}=6\) units in one hour
C empties \(5+4-6=3\) units in one hour
Time for C to empty the full tank \(\displaystyle =\frac{60}{3}=20\) hours
Pipe C alone empties the full tank in 20 hours.