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 hour 15 min 

(b) 2 hours 30 min 

(c) 3 hours 15 min 

(d) 4 hours 10 min

Answer 1

(a) 1 hour 15 min

Part of the tank emptied in 1 hour

= 1 - \(\big(\frac{1}{3}+\frac{4}{15}\big)\) = 1 - \(\frac{9}{15}\) = \(\frac{6}{15}\) = \(\frac{2}{5}\)

Time taken to empty the full tank = \(\frac{1}{\frac{2}{5}}\) = \(\frac{5}{2}\) hours

\(\therefore\) Time taken to empty the exactly half filled tank = \(\frac{1}{2}\times\frac{5}{2}\) hours = 1 hr 15 min.