Pipes A and B can fill a tank in 10 hours and 40 hours, respectively. C is an outlet pipe attached to the tank. If all the three pipes are opened simultaneously, it takes 80 minutes more time than what A and B together take to fill the tank. A and B are kept opened for 7 hours and then closed and C was opened. C will now empty the tank in:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 49 hours
We know that the efficiency is the reciprocal of the time taken
The efficiency of A & B be 1/10 & 1/40 units.
The efficiency when A & B work together = 1/10 + 1/40 = 5/40 = 1/8
The time taken by A & B together = 8 hours
If C is attached, where efficiency of C be 'x', then time taken is more 80 minutes which is = 8 + 80/60 = 28/3 hours
⇒ 1/10 + 1/40 - 1/x = 1/28/3
⇒ 1/x = 1/8 - 3/28
⇒ x = 56 hours
When A & B are opened for 7hours or filled 7/8 part the C will take time to empty will be
⇒ (7/8) × 56 = 49 hours