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Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in 3 and 4 h, respectively. The full cistern is emptied by the third tap in 5 h. If all three taps are opened simultaneously, the empty cistern will be filled up in ?
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- 114/23 h
- 214/23 h
- 2 h 40 min
- 1 h 56 min
Correct Option: B
Part of tank filled by first tap in 1 h = 1/3
Part of tank filled by second tap in 1 h = 1/4
Part of tank emptied by third tap in 1 h = 1/5
Part of the tank filled by all pipes opened simultaneously in 1 h
= 1/3 + 1/4 - 1/5 = (20 + 15 - 12)/60 = 23/60
Time taken by all the taps to fill the tank when it is empty = 23/60 h = 214/23 h
