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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 65% (02:46) correct 35% (02:33) wrong based on 51 sessions

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Competition Mode Question

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.

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Director  P
Joined: 18 May 2019
Posts: 528
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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Diameter of Tap A = 1cm, diameter of Tap B=4/3 cm, and diameter of Tap C=2cm. The largest tap, Tap C fills the cistern in 61 minutes.
We are informed that the amount of water flowing into the cistern is directly proportional to the square of the diameter of the tap. Hence the time to fill the cistern is inversely proportional to the diameter of the tap.

hence using proportionality, we can determine the time for Taps A and B, given time taken for Tap C=61minutes.
Time for A, ta = 61*4/1 = 144 minutes
Time for B, tb= 61*4*9/16 = 549/4 minutes

Hence the time taken when all three taps work together = ta*tb*tc/(ta*tb + ta*tc + tb*tc)
=1,205,604/56,745.25
=36minutes

Manager  G
Joined: 17 Jan 2019
Posts: 127
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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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.

the 2 extra pipes together is little bigger than the diameter of the largest one so it should be at least half faster, therefore, less than 30 minutes.
I would say A
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5436
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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3
1
from given info
dia === flow rate
1=====1
4/3====16/9
2======4
so largest dia 2 cm ; flow rate = 4 cm2/min vol of tank ; 4*61 ; 244 cm^3
since all three pipes are open together so total combined flow rate ; 1+16/9+4 = 61/9
time taken ; 61/9*x = 244
x= 36 mins
IMO D

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.
Director  P
Joined: 24 Nov 2016
Posts: 927
Location: United States
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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Quote:
In what time would a cistern be filled by three pipes whose diameters are 1 cm , 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.

$$(d_1)^2*(time_1)=(d_2)^2*(time_2)…time_1=61$$
$$(2)^2*(61)=(1)^2*(time_2)…4(61)=(time_2)…time_2=244$$
$$(2)^2*(61)=(4/3)^2*(time_2)…4(61)(9)/16=(time_3)…time_3=549/4$$

$$rate_n=\frac{1.cistern}{time_n}$$

$$\frac{1.cistern}{add.rates}=time.to.fill$$
$$time.to.fill=\frac{1}{1/61+1/244+1/549/4}=\frac{1}{5/244+4/549}=\frac{1}{5/(4*61)+4/(9*61)}=\frac{61}{5/4+4/9}=36$$

Senior Manager  G
Joined: 25 Jul 2018
Posts: 389
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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1
The rate of the amount of water flowing in by each pipe= 1 : 16/9 : 4

The capacity of cistern =x+(16/9)x+4x=(61/9)x
-->The largest one is 4x. It takes 61 minutes to fill the cistern alone.

All pipes started and finished at the same time.
So, finding the time which the largest one spent is enough to answer the question.

(61/9)x --> 61 minutes
4x ------> a minutes

--> a= (4x*61):(61/9)x= 36 minutes

Manager  S
Joined: 09 Nov 2015
Posts: 153
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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"The flow of water flowing in through each pipe is directly proportional to the square of the diameter of that pipe" which means that:
d^2*k=f (where 'd' is the pipe dia, 'k' is a constant and 'f' is the quantity of water flowing in per unit of time).
Let's assume the capacity of the cistern is 122 liters. So the largest pipe (2 cm dia) will fill @ 122/61=2 liters/minute. Then:
(2^2)*k=2....> k=1/2

The values of 'f' for the other two pipes can thus be determined as follows:
(4/3)cm dia: (4/3)^2*(1/2)=8/9 liters/minute
1 cm dia: 1^2*(1/2)=1/2 liters/minute

So when all 3 pipes work together, total inflow of water into the cistern per minute is 2+(8/9)+(1/2)=61/18 liters.
Time needed to fill 122 liters = 122/(61/18) = (122*18)/61 = 2*18 = 36 minutes.

ANS: D
Intern  Joined: 09 Oct 2019
Posts: 2
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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the amount of water flowing in by each pipe being proportional to the square of its diameter

water debit of three:
= 1^2 + (4/3)^2 + 2^2
= 1 + 16/9 + 5
= 61/9 cm^2

since 4 cm^2 needs 61 minutes, so
4 * 61 = 61/9 * T
T = 4*9
T = 36 minutes Re: In what time would a cistern be filled by three pipes whose diameters   [#permalink] 13 Oct 2019, 23:41
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