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Difficulty:
15%
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Question Stats:
83% (01:58) correct
17%
(02:04)
wrong
based on 333
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A group of 3 small pumps and 1 large pump is filling a tank. Each of the 3 small pumps works at 2/3 of the rate of the large pump. If all 4 pumps work at the same time, they will fill the tank in what fraction of the time that it would have taken the large pump had it operated alone?
A. 1/6
B. 1/3
C. 2/3
D. 3/4
E. 4/3
A. 1/6
B. 1/3
C. 2/3
D. 3/4
E. 4/3
04 Nov 2014, 00:58
Kudos
Bookmarks
Let the work done = 1
Let the rate of big pump = x
Time required by big pump \(= \frac{1}{x}\) ................ (1)
Rate of each small pump \(= \frac{2x}{3}\)
Combined rate of 3 small & 1 big pump \(= 3*\frac{2x}{3} + x = 3x\)
Time required (All 4 pumps combined) \(= \frac{1}{3x}\) ............. (2)
\(Fraction = \frac{\frac{1}{3x}}{\frac{1}{x}} = \frac{1}{3}\)
Answer = B
Let the rate of big pump = x
Time required by big pump \(= \frac{1}{x}\) ................ (1)
Rate of each small pump \(= \frac{2x}{3}\)
Combined rate of 3 small & 1 big pump \(= 3*\frac{2x}{3} + x = 3x\)
Time required (All 4 pumps combined) \(= \frac{1}{3x}\) ............. (2)
\(Fraction = \frac{\frac{1}{3x}}{\frac{1}{x}} = \frac{1}{3}\)
Answer = B
02 Nov 2014, 06:57
Kudos
Bookmarks
jgk
Since 1 small pump works at 2/3 of the rate 1 large pump, then 3 small pumps work at the rate of 3*2/3 = 2 large pumps.
Thus, 3 small pumps and 1 large pump together, work at the rate of 2 + 1 = 3 large pumps. Therefore, together they will do the job in 1/3 the time it would take the large pump to do the job alone.
Answer: B.
