Pipes and Cistern - Quantitative Aptitude (MCQ) questions for Q. 77

Q.  Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?
- Published on 12 Jun 15

a. 10 minutes
b. 15 minutes
c. 12 minutes
d. 9 minutes

ANSWER: 9 minutes
 
Let B be turned off after X minutes.

Part of water will be filled by A + B in x minutes + After tap B is closed rest filled by A in (30-x) minutes = 1

=> x/(time taken to fill the container by each separately) + 30 - x/(time taken to fill the container by A alone) = 1
=> x(2/75 + 1/45) + (30-x)2/75 = 1
=> 11x + 180 – 6x = 225

Therefore, x = 9 minutes

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