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

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Math Expert
Joined: 02 Sep 2009
Posts: 60496
In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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08 Oct 2019, 20:55
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55% (hard)

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65% (02:46) correct 35% (02:33) wrong based on 52 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.

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Posts: 5694
Location: India
Concentration: Sustainability, Marketing
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Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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09 Oct 2019, 03:44
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
Joined: 18 May 2019
Posts: 646
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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08 Oct 2019, 22:14
1
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

VP
Joined: 24 Nov 2016
Posts: 1070
Location: United States
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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09 Oct 2019, 04:49
1
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
Joined: 25 Jul 2018
Posts: 467
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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09 Oct 2019, 18:47
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
Joined: 17 Jan 2019
Posts: 140
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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08 Oct 2019, 23:16
1
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
Manager
Joined: 09 Nov 2015
Posts: 160
Re: In what time would a cistern be filled by three pipes whose diameters  [#permalink]

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11 Oct 2019, 02:23
"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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13 Oct 2019, 23:41
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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