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In what time would a cistern be filled by three pipes whose diameters

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In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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New post 21 Jan 2017, 09:23
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Difficulty:

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Question Stats:

63% (03:01) correct 38% (03:28) wrong based on 79 sessions

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In what time would a cistern be filled by three pipes whose diameters are 1cm , 4/3 cm , 2 cm,running together, when the largest alone will fill it in 61 minutes, the amount of water flowing in by each pipe being proportional to square of its diameter ??

A. 18 minutes
B. 20 minutes
C. 40 minutes
D. 36 minutes
E. 72 minutes.


Source :- Quicker Maths
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Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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New post 21 Jan 2017, 12:33
rohit8865 wrote:
In what time would a cistern be filled by three pipes whose diameters are 1cm , 4/3 cm , 2 cm,running together, when the largest alone will fill it in 61 minutes, the amount of water flowing in by each pipe being proportional to square of its diameter ??

A. 18 minutes
B. 20 minutes
C. 40 minutes
D. 36 minutes
E. 72 minutes.


Source :- Quicker Maths


This one gave a real headache.

Rate of 3 pipes working together:

\(\frac{1}{N}\), \(N = x + 4x + \frac{16x}{9} = \frac{61x}{9}\)

\(\frac{1}{N} = \frac{9}{61x}\)

Rate of the biggest pipe = \(\frac{1}{4x}\)

\(\frac{1}{4x} ---> 61 (min)\)

\(\frac{9}{61x} ----> y (min)\)

\(\frac{y}{4x} = \frac{9*61}{61x}\)

\(\frac{y}{4x} = \frac{9}{x}\)

\(y*x = 36*x\)

\(y = 36 min\)

Answer D
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In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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New post 21 Jan 2017, 13:03
rohit8865 wrote:
In what time would a cistern be filled by three pipes whose diameters are 1cm , 4/3 cm , 2 cm,running together, when the largest alone will fill it in 61 minutes, the amount of water flowing in by each pipe being proportional to square of its diameter ??

A. 18 minutes
B. 20 minutes
C. 40 minutes
D. 36 minutes
E. 72 minutes.


Source :- Quicker Maths


rate of largest pipe=1/61
rate of smallest pipe=(1/2)^2*1/61=1/(4*61)
rate of middle pipe=(2/3)^2*1/61=4/(9*61)
let t=time for all three pipes to fill cistern
1+1/4+4/9=61*1/t
61/36=61/t
t=36 minutes
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Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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Re: In what time would a cistern be filled by three pipes whose diameters   [#permalink] 08 Oct 2018, 04:17
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