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

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

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

\(rate_n=\frac{1.cistern}{time_n}\)

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

Answer (D)

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

The answer is D.

"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

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

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