Pipes and Cistern
 A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already half full and both the taps are opened together, the tank will be ?

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Part emptied in 1 min. = (1/8  1/16) = 1/16
∴ Time taken to empty the full tank = 16 min.Correct Option: D
Part emptied in 1 min. = (1/8  1/16) = 1/16
∴ Time taken to empty the full tank = 16 min.
Hence, time taken to empty the half tank = 8 min.
 One tap can fill a cistern in 2 hours and another can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened ?

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Net filling in 1 hour = (1/2  1/3) = 1/6
Correct Option: B
Net filling in 1 hour = (1/2  1/3) = 1/6
∴ Time taken to fill the cistern = 6 hours
 A cistern can be filled by two pipes A and B in 4 hours and 6 hours respectively. When full, the tank can be emptied by a third pipe C in 8 hours . If all the taps be turned on at the same time, the cistern will be full in ?

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Net filling in 1 hour = (1/4 + 1/6  1/8) = 7/24
Correct Option: B
Net filling in 1 hour = (1/4 + 1/6  1/8) = 7/24
∴ Time taken to fill the cistern = (24/7) hrs. = 3 hrs. 26 min.
 A pipe can fill a tank in x hours and another can empty it in y hours. They can together fill it in (y > x) ?

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Net filling in 1 hour = (1/x  1/y) = (y  x) / xy
Correct Option: D
Net filling in 1 hour = (1/x  1/y) = (y  x) / xy
∴ Time taken to fill the tank = xy / (y  x) hrs.
 Three pipes A, B and C can fill a tank separately in 8 h,10 h and 20h, respectively. Find the time taken by all the three pipes to fill the tank when these pipes are opened together ?

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Part filled by A in 1 h = 1/8
Part filled by B in 1 h = 1/10
Part filled by C in 1 h = 1/20
Part filled by (A + B + C) in 1 h = 1/8 + 1/10 + 1/20Correct Option: D
Part filled by A in 1 h = 1/8
Part filled by B in 1 h = 1/10
Part filled by C in 1 h = 1/20
Part filled by (A + B + C) in 1 h = 1/8 + 1/10 + 1/20
= (5 + 4 + 2)/40 = 11/40
∴ Required time to fill the tank = 40/11 h
= 3^{7}/_{11} h