Q14. 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 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:
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Total work = 40
Time taken to fill the tank A and B together = 40/(1 + 4) = 8 hrs
Let the efficiency of C be x.
If all three pipe A, B and outlet pipe C open, time taken to fill the tank = 8 hr + 80 min = 9 + 1/3 = 28/3 hrs
Efficiency of A, B and C = 40/(28/3) = 30/7
According to the question
4 + 1 + x = 30/7
⇒ x = 30/7 – 5
⇒ x = (–5/7)
Work done by A and B in 7 hrs = (4 + 1) × 7 = 35
∴ Pipe C empty the tank filled by A and B in 7 hrs = 35/(5/7) = 49 hrs
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