Question

A tank can be filled by two pipes A and B separately in 3 hours and 3 hours 45 minutes respectively, A third pipe C can empty the full tank in 1 hour, when the tank was exactly half-filled, all the three pipes are opened. The tank will become empty in

• A. 1 hours 15 min
• B. 2 hours 30 min
• C. 3 hours 15 min
• D. 4 hours 10 min

Answer 1

Answer: (A)

1 hours 15 min

Part of the tank emptied in 1 hour = 1 - $(\frac{1}{3}+\frac{4}{15})=1-\frac{9}{15}=\frac{6}{15}=\frac{2}{5}$
$(\because 3hrs45min=3\frac{45}{60}=\frac{15}{4}hrs)$
Time taken to empty the full tank = $\frac{1}{\frac{2}{5}}=\frac{5}{2}hrs$
$\therefore$ Time taken to empty the exactly half filled tank = $\frac{1}{2}\times \frac{5}{2}hours=\frac{5}{4}hours=1hr15min$