# Pipes and Cistern ( 11 to 15 )

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Pipes and Cistern ( 11 to 15 ):

# APTITUDE QUESTIONS (PIPES AND CISTERN):

11. Two pipes X and Y together can fill a cistern in 4 hours. If both the pipes had been opened separately, then Y would have taken 6 hours more than X to fill the cistern. How much time will be taken by X to fill the cistern separately?

A)    1 hr

B)    2 hrs

C)    6 hrs

D)    8 hrs

E)    None of these

Explanation:

Let the cistern be filled by pipe X alone in x hours.

Then, pipe Y will fill it in (x + 6) hrs

∴ 1/x + 1/(x+6) = 1/4 <=> (x+6+x)/(x(x+6)) = 1/4

<=> x2 – 2x – 24 = 0 <=> (x – 6) (x + 4) = 0

<=> x = 6

12. One pipe can fill a tank three times as fast as another pipe. If both pipes can fill the tank in 40 minutes, then the slower pipe alone will be able to fill the tank in:

A)    181 min

B)    180 min

C)    160 min

D)    192 min

E)    None of these

Explanation:

Let consider that slower pipe alone fill the tank in x minutes.

So, faster pipe will fill it in x/3 minutes.

∴ 1/x + 3/x = 1/40 <=> 4/x = 1/40 <=> x = 160 min.

13. A tank is filled in 5 hours by three pipes X, Y and Z. Z pipe is twice as fast as Y and Y is twice as fast as X.

A)    20 hrs

B)    25 hrs

C)    35 hrs

D)    30 hrs

E)    None of these

Explanation:

Suppose pipe X alone takes x hours to fill the tank.

Then, pipes Y and Z will take x/2 and x/4 hours respectively to fill the tank

∴ 1/x + 2/x + 4/x = 1/5  <=>  7/x = 1/5  <=>  x = 35 hrs

14. A tank is filled by three pipes with uniform flow. The first two pipes operate simultaneously and fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe will fill the tank in 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:

A)    16 hrs

B)    10 hrs

C)    15 hrs

D)    30 hrs

E)    None of these

Explanation:

Suppose first pipe alone takes x hours to fill the tank. Then, second pipe and third pipe will take (x – 5) and (x – 9) hours respectively to fill the tank.

∴ 1/x + 1/(x-5) = 1/(x-9) <=> x-5+x/x(x-5)=1/(x-9)

<=> (2x – 5) (x – 9) = x (x – 5)     <=> x2 – 18x + 45 = 0

<=> (x – 15) (x – 3) = 0      <=> x = 15

15. 12 buckets of water fill a tank when the capacity of each tank is 13.5 ltrs. If the capacity of each bucket is 9 litres then how many buckets will be needed to fill the same tank?

A)    10

B)    15

C)    16

D)    18

E)    None of these

Explanation:

Capacity of the tank = (12 * 13.5) litres = 162 litres

Capacity of each bucket = 9 litres

Number of buckets required = (162/9) = 18