Pipe P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all the three are opened at 7 am, at what time will one-fourth of the tank be filled?
[A]10 am
[B]11 am
[C]10 pm
[D]11 pm

10 pm
Part of tank filled in 1 hour when all three pipes are opened
$= \frac{1}{10}+\frac{1}{12}-\frac{1}{6}$
$= \frac{6+5-10}{60} = \frac{1}{60}$
∴ The tank will be filled in 60 hours.
∴ One fourth of the tank will be filled in 15 hours so the tank will be filled at 10 pm.
Hence option [C] is correct answer.