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

Ans. empty in 45 minutes

explanation::

Let the capacity of the tank = LCM of (12,15, 6) = 60 litres.

Rate of work done by the first pipe = 60/12

⇒ 5 L/min

Rate of work done by the second pipe = 60/15

⇒ 4L/min

Rate of work done by the draining pipe = 60/6

⇒10L/min

If all the pipes are opened simultaneously, (5+4-10) litres will be filled in a minute.

Since this comes out to be negative, no water will be filled at any point of time.

for 5 min only filling pipes r opened

Rate of both filling pipes = 9L/min, (5+4).

So in 5 minutes, 9 × 5 = 45 litres water is filled.

When the third pipe is opened, all three pipes will work simultaneously, at a rate of (5+4 – 10) = - 1 ltr per min. This implies that in a minute, 1 litre water will be drained.

So, 45 litres water will be drained in 45 minutes. So the tank will be emptied in 45minutes.