100+ Pipes and Cisterns Problems with Solutions Pdf - 1

 Question: 1

A tap can completely fill a water tank in 8 hours. The water tank has a hole in it through which the water leaks out. The leakage will cause the full water tank to get empty in 12 hours. How much time will it take for the tap to fill the tank completely with the hole?

(A) 8 hours

(B) 16 hours

(C) 18 hours

(D) 24 hours

View Answer

Ans: D

Net part filled in 1 hour = (

1

8

–

1

12

) = 

1

24

∴ The tank will be filled in 24 houirs.

Question: 2

Two pipes A and B can fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is one third full, a leak develops in the tank through which one third water supplied by both the pipes goes out. The total time taken to fill the tank is

(A) 12 hours

(B) 16 hours

(C) 18 hours

(D) 20 hours

View Answer

Ans: B

Part filled by (A + B) in 1 hour = (

1

20

+

1

30

) = 

1

12

.

So, A and B together can fill the tank in 12 hrs.

1

3

 part is filled by (A + B) in (

1

3

×12) = 4 hrs.

Since the leak empties one third water, so time taken to fill the tank = Time taken by (A + B) to fill the whole tank + Time taken by (A + B) to fill one – third tank = (12 + 4) hrs = 16 hrs.

Question: 3

An outlet pipe can empty a cistern in 3 hours. In what time will the empty 

2

3

 part of the cistern?

(A) 2 hours

(B) 3 hours

(C) 4 hours

(D) 5 hours

View Answer

Ans: B

The outlet pipe empties the one complete cistern in 3 hours.

∴ Time taken to empty 

2

3

Part of the cistern = 

2

3

×3 = 2 hours.

Question: 4

A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

(A) 5 hrs

(B) 6.5 hrs

(C) 7.2 hrs

(D) 9.1 hrs

View Answer

Ans: C

Net part filled in 1 hour = (

1

4

–

1

9

) = (

5

36

)

∴ The cistern will be filled in 

36

5

 hrs i.e., 72 hrs.

Question: 5

12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

(A) 10

(B) 14

(C) 18

(D) 22

View Answer

Ans: C

Capacity of the tank = (12 × 13.5) litres = 162 litres.

Capacity of each bucket = 9 litres.

Number of buckets needed = (

162

9

) = 18.

Question: 6

In 1 minute, 

3

7

 of a bucket is filled. The rest of the bucket can be filled in

(A) 

4

3

 minutes

(B) 

7

3

 minutes

(C) 

7

4

 minutes

(D) None of these

View Answer

Ans: A

Time taken to fill the whole bucket = 

7

3

 min.

∴ Required time = (

7

3

−1) minutes = 

4

3

 minutes.

Question: 7

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) 80 gallons

(C) 100 gallons

(D) 120 gallons

View Answer

Ans: D

Work done by the waste pipe in 1 minute

= 

1

15

 – (

1

20

+

1

24

) = (

1

15

–

11

120

) = - 

1

40

[-ve sign means emptying]

∴ Volume of 

1

40

 part = 3 gallons.

Volume of whole tank = (3 × 4) gallons = 120 gallons.

Question: 8

A pump can fill a tank with water in 2 hours. Because of a leak, it took 2

1

3

 hours to fill the tank. The leak can drain all the water of the tank in

(A) 7 hrs

(B) 8 hrs

(C) 14 hrs

(D) 20 hrs

View Answer

Ans: C

Work done by the leak in 1 hour = (

1

2

–

3

7

) = 

1

14

.

Leak will empty the tank in 14 hrs.

Question: 9

A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?

(A) 7580

(B) 7960

(C) 8290

(D) 8640

View Answer

Ans: D

Work done by the inlet in 1 hour = (

1

8

–

1

12

) = 

1

24

Work done by the inlet in 1 min. = (

1

24

×

1

60

) = 

1

1440

Volume of 

1

1440

 part = 6 litres.

Volume of whole = (1440 × 6) litres = 8640 litres.

Question: 10

Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?

(A) 2

(B) 3

(C) 4

(D) 5

View Answer

Ans: B

Part filled by (A + B + C) in 1 hour = (

1

5

+

1

10

+

1

30

) = 

1

3

∴ All the three pipes together will fill the tank in 3 hours.