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Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would take taken 6 hours more than A fill the cistern. How much time will be taken by A to fill the cistern separately?

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Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would take taken 6 hours more than A fill the cistern. How much time will be taken by A to fill the cistern separately?
1). 6 hours
2). 8 hours
3). 10 hours
4). 12 hours


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1 answers

3 vote
Answered by on | Votes 3 |

⇒ Let the cistern be filled by pipe A alone in x hours.

⇒ Then, pipe B will fill it in (x + 6) hours

⇒ 1/x + 1/(x + 6) = ¼ (x + 6 + x)/(x (x + 6)) = 1/4

⇒ x2 - 2x - 24 = 0 (x - 6) (x + 4) = 0

⇒ x = 6, - 4 [Ignoring the -ve value of x]

X = 6 hours will be the required ans.

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