Pipes A and B can fill a tank in 10 hours and 40 hours respectively C is an outlet pipe attached to ...........

Quantitative Aptitude (CGL) Pipes&cistern

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:

This questions was previously asked in

SSC CGL 5th March 2020 Shift-1

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49 hours

38.5 hours

42 hours

45.5 hours

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Explanation:

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 = $$\frac{35}{5/7} = 49$$

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