Question

Two pipes A and B can fill a cistern is 12 minutes and 15 minutes respectively but a third pipe C can empty the full tank in 6 minutes. A and B are kept open for 5 minutes in the beginning and then C is also opened. In what time will the cistern be emptied? 

(a) 30 min

(b) 33 min

(c) 37.5 min

(d) 45 min

Answer 1

Correct option is (d) 45 min

Part filled in 5 min = \(5 \times\left(\frac 1{12} + \frac 1{15}\right)\)

\(= 5\times\frac 9{60} \)

\(= \frac 34\)

Part emptied in 1 minute when all the pipes are opened = \(\frac 16 - \left(\frac 1{12} + \frac 1{15}\right) \)

\(= \frac 1{60}\)

Now, \(\frac 1{60}\)​ part is emptied in 1 minute.

Therefore, \(\frac 34\)​ part will be emptied in 60 × \(\frac 34\)​ = 45 minutes.