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A group of four pumps is designed to fill a tank such that each of the
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22 Dec 2024, 22:38
22 Dec 2024, 22:38
Expert Reply
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Question Stats:
33% (01:57) correct
66% (01:45) wrong based on 3 sessions
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A group of four pumps is designed to fill a tank such that each of the three pumps work at $\(\frac{2}{3}\)$ rd the rate of the fourth pump. If all 4 pumps work at the same time, they should fill the tank in what fraction of the time taken by the fourth pump working alone?
(A) $\(\frac{1}{6}\)$
(B) $\(\frac{1}{5}\)$
(C) $\(\frac{1}{3}\)$
(D) $\(\frac{2}{5}\)$
(E) $\(\frac{1}{2}\)$
(A) $\(\frac{1}{6}\)$
(B) $\(\frac{1}{5}\)$
(C) $\(\frac{1}{3}\)$
(D) $\(\frac{2}{5}\)$
(E) $\(\frac{1}{2}\)$
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A group of four pumps is designed to fill a tank such that each of the
[#permalink]
02 Feb 2025, 06:46
02 Feb 2025, 06:46
Expert Reply
OE
Let the speed of the largest pump be 's', so the speed of the each of the three pumps would be $\(\frac{2}{3}\)$ of the largest pump's speed $\(=\frac{2 s}{3}\)$.
So, the combined speed of all 4 pumps comes out to be $\(s+3 ( \frac{2s}{3} )\)$ which gives the time taken by all 4 pumps together to fill the tank as $\(\frac{1}{3 s}\)$ Work done $=$ Speed $\times$ Time $)$
The time taken by the largest pump alone to fill the tank is $\(\frac{1}{s}\)$
Finally the time taken by all 4 pumps together to fill the $\( \frac{\frac{1}{3s}}{\frac{1}{s}}=\frac{1}{3}\)$ of the time taken by the largest pump alone to fill the tank.
Hence the answer is (C).
Let the speed of the largest pump be 's', so the speed of the each of the three pumps would be $\(\frac{2}{3}\)$ of the largest pump's speed $\(=\frac{2 s}{3}\)$.
So, the combined speed of all 4 pumps comes out to be $\(s+3 ( \frac{2s}{3} )\)$ which gives the time taken by all 4 pumps together to fill the tank as $\(\frac{1}{3 s}\)$ Work done $=$ Speed $\times$ Time $)$
The time taken by the largest pump alone to fill the tank is $\(\frac{1}{s}\)$
Finally the time taken by all 4 pumps together to fill the $\( \frac{\frac{1}{3s}}{\frac{1}{s}}=\frac{1}{3}\)$ of the time taken by the largest pump alone to fill the tank.
Hence the answer is (C).
gmatclubot
A group of four pumps is designed to fill a tank such that each of the [#permalink]
02 Feb 2025, 06:46
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