### Pipes and Cistern Questions and Answers

#### Article

Q 1

A pipe can fill a tank in an hour. Because of a leak, it took 1 hour and 10 minutes to fill the tank. Find the time taken by the leak to drain all the water in the tank.

A)

10 minutes

B)

7/6 hours

C)

6/7 hours

D)

7 hours

Correct Option - D

Explanation

Let the leak take x hours to drain the tank.

1 hr 10 min = 1+(1/6) = 7/6 hrs

1-(1/x) = 1/(7/6) = 6/7

Part of tank leaked in an hour = 1-6/7 = 1/7

The leak takes 7 hours to drain all the water.

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Q 2

Pipe A and Pipe B can fill a tank in 1 hour and 1 ¼ hours respectively. Both pipes are opened in the beginning and after some time, pipe B is closed. The tank is filled in 40

A)

30 minutes

B)

45 minutes

C)

40 minutes

D)

25 minutes

Correct Option - D

Explanation

Part of tank filled by A in a minute

= 1/60

Part of tank filled by B in a minute

= 1/75

Let pipe B be closed after x minutes.

Part of tank filled in x minutes

= x*[(1/60)+(1/75)]

= 9x/300

Part of tank filled in (40-x) minutes

= [(40-x)*(1/60)]

= (40-x)/60

(9x/300) + ((40-x)/60) = 1

4x = 100

x = 25

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Q 3

Two taps A and B can fill a bathtub in 10 minutes and 15 minutes respectively. If A was open for the first two minutes, B for the next two minutes and so on, the bathtub is

A)

6 minutes

B)

12 minutes

C)

12.5 minutes

D)

24 minutes

Correct Option - B

Explanation

Part of the tub filled in the first 2 minutes

= 2*1/10 = 1/5

Part of the tub filled in the next 2 minutes

= 2*1/15 = 2/15

Part of the filled in 4 minutes

= (1/5) + (2/15) = 1/3

Time required to fill the tub

= 3*4 = 12 minutes

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Q 4

Two pipes A and B can fill a tank in 20 minutes when opened simultaneously. If pipe A alone takes 60 minutes to fill the tank, how much time will pipe B alone take to fill the

A)

60 minutes

B)

40 minutes

C)

30 minutes

D)

20 minutes

Correct Option - C

Explanation

Let B take x minutes to fill the tank.

Part of the tank filled by A and B

= (1/60) + (1/x) = (1/20)

Solving this, x=30

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Q 5

A tank has three inlets A, B and C. C takes twice the time taken by A to fill the tank and B takes half the time taken by A to fill the tank. If they can fill the tank together in 4

A)

7 minutes

B)

14 minutes

C)

3.5 minutes

D)

28 minutes

Correct Option - A

Explanation

Let A take x minutes to fill the tank.

(1/x) + (1/(x/2)) + (1/2x) = 1/4

(7/2x) = ¼

x = 14

x/2 = 7

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Q 6

An inlet pipe fills a tank at the rate of 5 litres of water a minute. An outlet connected to the tank can empty a full tank in 5 hours. Both the pipes are opened together for 30

A)

480 liters

B)

360 liters

C)

300 liters

D)

240 liters

Correct Option - C

Explanation

Let the inlet pipe take x minutes to fill the tank.

Part of the tank filled by the inlet in a minute

= (1/x)

Part of the tank emptied by the outlet in a minute

= 1/(5*60) = 1/300

Part of the tank filled in the first 30 minutes

= 30*[(1/x)-(1/300)]

= (300-x)/10x

Part of the tank filled in the next 36 minutes

= 36*(1/x)

1 – [(300-x)/10x] = 36/x

Solving, x = 60

Capacity of the tank = 60*5 = 300 liters

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Q 7

Pipe A and Pipe B can fill a tank in 20 minutes and 30 minutes respectively. Pipe C can empty the tank in 60 minutes.  The tank is initially empty. Both the pipes A and B are

A)

12 minutes

B)

13.5 minutes

C)

15 mintes

D)

14.5 minutes

Correct Option - B

Explanation

1/20th of the tank is filled by Pipe A in 1 minute.

1/30th of the tank is filled by Pipe B in 1 minute.

1/60th of the tank is emptied by Pipe C in 1 minute.

Part of tank filled in the first 6 minutes = 6*[(1/20)+(1/30)] = 1/2

When all pipes are opened, part of tank filled in 1 minute = (1/12)-(1/60) = 1/15

Time required to fill the remaining ½ of the tank = (1/2)/(1/15) = 7.5

Total time = 6+7.5 = 13.5 minutes