A cistern can be filled by two pipes in 10 and 12 min respectively. Both the pipes are opened together for a certain time but, due to defects, only 1/6th of full quantity of water flows through the former and 2/5th of the latter. The defects are detected and rectified. The cistern is filled in 3 min from that moment. How long was it before the detects were rectified?
1). 8 min
2). 8.5 min
3). 9 min
4). 10 min
Pipe A can fill the tank in 10 min.
Pipe B can fill the tank in 12 min.
Total units to be filled in the cistern = LCM of (10, 12) = 60
⇒ Pipe A can fill 6 units of water in 1 min.
⇒ Defected Pipe A can fill (6 × 1/6) = 1 unit of water in 1 min.
⇒ Pipe B can fill 5 units of water in 1 min.
⇒ Defected Pipe B can fill (5 × 2/5) = 2 units of water in 1 min.
Given that, last 3 min, both the pipes used were rectified
⇒ in last 3 min (6 + 5) × 3 = 33 units of water were filled in the tank.
⇒ (60 - 33) = 27 units of water were filled with defected pipes.
Both Defected pipes can fill 3 units of water in 1 min.
⇒ Defected pipes can fill 27 units of water in (27/3) = 9 min.
∴ After 9 minutes the defects were rectified.