A cistern can be filled by two pipes filling separately in 12 and 16 min respectively. Both pipes are opened together for a certain time but being closed, only 7/8 of the full quantity of water flows through the former and only 5/6 through the latter pipe. The obstruction however being suddenly removed the cistern is filled in 3 min from that moment. How long was it before the full flow began?
A cistern can be filled by two pipes filling separately in 12 and 16 min respectively. Both pipes are opened together for a certain time but being closed, only 7/8 of the full quantity of water flows through the former and only 5/6 through the latter pipe. The obstruction however being suddenly removed the cistern is filled in 3 min from that moment. How long was it before the full flow began?
1). 2.5 min
2). 4.5 min
3). 3.5 min
4). 5.5 min
1 answers
Let the pipe be opened for x min
⇒ Work done in 1 min by first pipe = 1/12
⇒ Work done in 1 min by second pipe = 1/16
⇒ Work done by both in 3 min = 3 × {(1/12) + (1/16)} = 21/48
⇒ Remaining work i.e. 27/48 is done by (7/8) first pipe and (5/6) second pipe
⇒ x × [{(7/8) × (1/12)} + {(5/6) × (1/16)} = 27/48
⇒ (1/8) x = 27 / 48
∴ x = 4.5 min