A cistern can be filled by pipes a and b in 12 minutes and 10 minutes respectively . the full tank can be emptied by a third pipe c in 8 minutes only .if all the pipes be turned on at the same time,the cistern will be full in : *
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Hey there!!
Pipe a = 12 min
Pipe b = 10 min
Pipe c = 8 min ( emptying )
Pipe a in 1 minute = 1 / 12
Pipe b in minute = 1 / 10
Pipe c = 1 / 8
a and b fill, c empties
So,
1 / a + 1 / b - 1 / c = Tank filled in one minute
1 / 12 + 1 / 10 - 1 / 8
LCM = 120
10 / 120 + 12 / 120 - 15 / 120
10 + 12 - 15 / 120
22 - 15 / 120
7 / 120 = Filled in one minute
Total time = 120 / 7
Total time taken to fill the cistern = 17.14 minutes ( approx )
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