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Pipes and Cistern - General Aptitude

Q1:

Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

A 5 min.

B 9 min.

C 10 min.

D 15 min.

ANS:B - 9 min.

Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.

x 2 + 1 + (30 - x). 2 = 1
75 45 75
11x + (60 -2x) = 1
225 75
11x + 180 - 6x = 225. x = 9.