Taps X and Y can fill a tank in 30 and 40 minutes respectively Tap Z can empty the filled tank in 60...........

Quant (SSC) Pipes&cistern

Taps X and Y can fill a tank in 30 and 40 minutes respectively.Tap Z can empty the filled tank in 60 minutes.If all the three taps are kept open for one minute each,how much time will the taps take to fill the tank?

48min

72min

24min

None of these

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Explanation:

Given taps X and Y can fill the tank in 30 and 40 minutes respectively. Therefore,
part filled by tap X in 1 minute = 1/30
part filled by tap Y in 1 minute = 1/40
Tap Z can empty the tank in 60 minutes. Therefore,
part emptied by tap Z in 1 minute = 1/60
Net part filled by Pipes X,Y,Z together in 1 minute = [1/30 +1/40 - 1/60] = 5/120 = 1/24
i.e., the tank can be filled in 24 minutes.