pipes and cistern aptitude questions

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6. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
A. 60 gallons B. 100 gallons
C. 120 gallons D. 180 gallons

Answer: Option C

Explanation:

 

 

Work done by the waste pipe in 1 minute = 1 – 1 + 1
15 20 24

 

    = 1 – 11
15 120

 

    = – 1 .    [-ve sign means emptying]
40

 

Volume of 1 part = 3 gallons.
40

Volume of whole = (3 x 40) gallons = 120 gallons.
7. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
A. 20 hours B. 25 hours
C. 35 hours D. Cannot be determined
E. None of these

Answer: Option C

Explanation:

 

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

 

Then, pipes B and C will take x and x hours respectively to fill the tank.
2 4

 

1 + 2 + 4 = 1
x x x 5

 

7 = 1
x 5

x = 35 hrs.
8. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
A. 1 hour B. 2 hours
C. 6 hours D. 8 hours

Answer: Option C

Explanation:

 

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

Then, pipe B will fill it in (x + 6) hours.

 

1 + 1 = 1
x (x + 6) 4

 

x + 6 + x = 1
x(x + 6) 4

x2 – 2x – 24 = 0

(x -6)(x + 4) = 0

x = 6.     [neglecting the negative value of x]
9. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A. 12 min B. 15 min
C. 25 min D. 50 min

Answer: Option A

Explanation:

 

 

Part filled by A in 1 min = 1 .
20

 

Part filled by B in 1 min = 1 .
30

 

Part filled by (A + B) in 1 min = 1 + 1 = 1 .
20 30 12

Both pipes can fill the tank in 12 minutes.
10. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
A. 10 min. 20 sec. B. 11 min. 45 sec.
C. 12 min. 30 sec. D. 14 min. 40 sec.

Answer: Option D

Explanation:

 

 

Part filled in 4 minutes = 4 1 + 1 = 7 .
15 20 15

 

Remaining part = 1 – 7 = 8 .
15 15

 

Part filled by B in 1 minute = 1
20

 

1 : 8 :: 1 : x
20 15

 

x = 8 x 1 x 20 = 10 2 min = 10 min. 40 sec.
15 3

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
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