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Four inlet pipes with circular cross section, take 9 hrs to fill a cis

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Bunuel
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Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   28 Dec 2019, 01:41
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Four inlet pipes with circular cross section, take 9 hrs to fill a cistern. How many pipes of half the radius are required to fill the cistern in 6 hrs if the speed of water now is three times the speed of water in the previous case?

A. 2
B. 4
C. 6
D. 8
E. 10
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D
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Re: Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   28 Dec 2019, 06:55
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Bunuel wrote:
Four inlet pipes with circular cross section, take 9 hrs to fill a cistern. How many pipes of half the radius are required to fill the cistern in 6 hrs if the speed of water now is three times the speed of water in the previous case?

A. 2
B. 4
C. 6
D. 8
E. 10


rate = 4/9
and in 6hrs @ 3 times speed we get
4/9 *6* 3 = 8
IMO D
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Re: Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   29 Dec 2019, 04:34
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Given
    • Four inlet pipes with circular cross section, take 9 hrs to fill a cistern

To find
    • The number of pipes of half the radius are required to fill the cistern in 6 hrs if the speed of water now is three times the speed of water in the previous case

Approach and Working out
If each pipe has a radius r and uniform filling speed is v, then
    • Total volume of water = π\(r^2\) x v x 4 x 9

Now, in the new case, each pipe has radius r/2, filling speed is 3v. If number of pipes is n then,
    • Total volume of water = π\((\frac{r}{2})^2\) x 3v x n x 6

Hence, we can write
    • π\((\frac{r}{2})^2\) x 3v x n x 6 = π\(r^2\) x v x 4 x 9
    Or, n = 8

Thus, option D is the correct answer.

Correct Answer: Option D
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Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   Updated on: 05 Jan 2020, 10:15
Bunuel wrote:
Four inlet pipes with circular cross section, take 9 hrs to fill a cistern. How many pipes of half the radius are required to fill the cistern in 6 hrs if the speed of water now is three times the speed of water in the previous case?

A. 2
B. 4
C. 6
D. 8
E. 10


When radius is halved then area becomes 1/4 hence after radius has been halved then the time taken will increase 4 times (NOT 2 times ).

So initially each pipe was taking 36 hrs after radius was halved each pipe started taking 36*4 =144 hrs but now speed was increased 3 times hence time will again reduce by 1/3 hence now each pipe will take \(\frac{144}{3}= 48\) hrs.

Now if we are to make sure that the whole work is done is 6 hrs instead of 48 hours we will be 8 pipes (8*6 =48 ).
Ans- D

Originally posted by stne on 05 Jan 2020, 07:40.
Last edited by stne on 05 Jan 2020, 10:15, edited 1 time in total.
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Nikhilgaur29
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Re: Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   05 Jan 2020, 08:17
9 x 4 x speed x πr^2 = Y x 6 x 3(speed) x πr^2/4

Y = 8

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Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   29 Jun 2020, 00:42
Bunuel wrote:
Four inlet pipes with circular cross section, take 9 hrs to fill a cistern. How many pipes of half the radius are required to fill the cistern in 6 hrs if the speed of water now is three times the speed of water in the previous case?

A. 2
B. 4
C. 6
D. 8
E. 10


the volume of cistern= volume of water pour by 4 pipes= 4*9*pie*\(r^2\)*v

now, r becomes \(\frac{r}{2}\) and v becomes 3v

the volume of cistern=the volume of water pour by n pipes = n*6*pie* \(\frac{r}{2}\)^2 *3v

now equate the equation as the volume of cistern not gonna change
calculate the value of n

4*9*pie*\(r^2\)*v = n*6*pie* \(\frac{r}{2}\)^2 *3v

n=8
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Re: Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   29 Jun 2020, 08:31
4 pipes could fill it in 9 hrs. If we half the radius, the efficiency of new pipes will reduce by 4 times. So in 9 hours now we need 4x4 = 16 such pipes to do the same task. So in 6 hours we need (16x9/6) = 24 such pipes. But, we also know we have 3 times more water coming now in the same time so now the same work can be done by 1/3 of the original required pipes = 24/3, 8 pipes.

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Re: Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink] New post   26 Jan 2022, 10:43
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Re: Four inlet pipes with circular cross section, take 9 hrs to fill a cis [#permalink]
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