Question 73

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:

Name: 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:
Uploaded: March 3, 2021, 3:45 p.m.
Duration: 5 min 4 s
Description: 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:

Solution

Let the total work be 40 units.

$$(\because$$ L.C.M. of 10 and 40 is 40.)

Efficiency of A = work/time = 40/10 = 4 units/hour

Efficiency of B = 40/40 = 1 unit/hour

Time time taken by pipe A and B = $$\frac{40}{4 + 1}$$ = 8 hours

Time time taken by pipe A, B and C together = 8 hours + 80/60 hours = 28/3 hours

Efficiency of A, B and C together = $$\frac{40}{28/3}$$ = 30/7 units/hour
Efficiency of C alone = 30/7 - 5 = -5/7 (- as pipe C is an outlet pipe and does negative work)

Work done by pipe A and B in 7 hours = (1 + 4)$$\times $$7 = 35 units

Time taken by pipe C to empty the tank = $$\frac{35}{5/7} = 49$$