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

Question

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

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

Archit3110 · Answer

rate = 4/9
and in 6hrs @ 3 times speed we get
4/9 *6* 3 = 8 
IMO D

EgmatQuantExpert · Answer

Solution

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

stne · Answer

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

Nikhilgaur29 · Answer

9 x 4 x speed x πr^2 = Y x 6 x 3(speed) x πr^2/4

Y = 8

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HouseStark · Answer

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

Anu5162 · Answer

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.

Posted from my mobile device

Posted from my mobile device

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=82926 Harsha GMAT Tutor | gmatanchor.com GMAT-Club-Forum-2uz3faff.png

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

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

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