Pipes And Cisterns MCQs

Pipe A can fill a tank in 12 hours and Pipe B can fill the same tank in 18 hours. If both pipes are opened simultaneously, how long will they take to fill the tank completely?

8 2/5 hours
7 1/5 hours
6 1/2 hours
5 3/4 hours

Explanation: When two pipes work together, their combined rate is the sum of individual rates. If Pipe A fills at 1/12 of the tank per hour and Pipe B at 1/18 per hour, their combined rate is 1/12 + 1/18 = 5/36 of the tank per hour. Therefore, time to fill one full tank is the reciprocal: 36/5 = 7 1/5 hours.

A fill pipe can fill a cistern in 8 hours while a waste pipe can empty it in 12 hours. If both pipes are opened together when the cistern is empty, how long will it take to fill the cistern?

24 hours
18 hours
16 hours
20 hours

Explanation: When one pipe fills and another empties simultaneously, the net filling rate is the difference of their individual rates. The fill pipe contributes 1/8 of the cistern per hour and the waste pipe removes 1/12 per hour. Net rate = 1/8 - 1/12 = 1/24 of the cistern per hour. The reciprocal gives the time to fill: 24 hours.

Pipes A and B can fill a tank in 6 hours and 8 hours respectively, while Pipe C can empty the full tank in 12 hours. If all three pipes are opened together, how long will it take to fill the empty tank?

6 2/3 hours
5 1/2 hours
4 4/5 hours
3 3/4 hours

Explanation: With multiple pipes operating simultaneously, add the filling rates and subtract the emptying rate. Pipe A fills at 1/6 per hour, Pipe B at 1/8 per hour, and Pipe C empties at 1/12 per hour. Net rate = 1/6 + 1/8 - 1/12 = 5/24 of the tank per hour. Time to fill = reciprocal = 24/5 = 4 4/5 hours.

Pipe A can fill a tank in 10 hours and Pipe B can fill it in 15 hours. Pipe A is opened first and after 2 hours, Pipe B is also opened. How long will it take to fill the tank completely from the start?

7 1/2 hours
6 4/5 hours
8 1/5 hours
5 3/5 hours

Explanation: First calculate the portion filled by Pipe A alone: in 2 hours it fills 2/10 = 1/5 of the tank. The remaining 4/5 of the tank is filled by both pipes working together at a combined rate of 1/10 + 1/15 = 1/6 per hour. Time to fill the remaining portion = (4/5) ÷ (1/6) = 24/5 = 4 4/5 hours. Total time = 2 + 4 4/5 = 6 4/5 hours.

A pipe can fill a tank in 8 hours. Due to a leak at the bottom, it takes 10 hours to fill the tank. How long would the leak take to empty a full tank?

32 hours
45 hours
36 hours
40 hours

Explanation: The pipe's filling rate is 1/8 of the tank per hour. With the leak present, the effective rate drops to 1/10 per hour. The leak's emptying rate is the difference: 1/8 - 1/10 = 1/40 of the tank per hour. Therefore, a full tank would be emptied by the leak alone in 40 hours.

Two pipes can fill a tank in 20 minutes and 30 minutes respectively. Both are opened together, but the second pipe is turned off after some time. If the tank is filled in 18 minutes total, after how many minutes was the second pipe turned off?

4 minutes
6 minutes
5 minutes
3 minutes

Explanation: Let the second pipe operate for x minutes. The first pipe runs for the full 18 minutes, filling 18/20 of the tank. The second pipe fills x/30 of the tank. Together they fill the whole tank: 18/20 + x/30 = 1. Solving: 9/10 + x/30 = 1, so x/30 = 1/10, giving x = 3 minutes.

A fill pipe can fill a tank in 12 hours and a waste pipe can empty it in 8 hours. The tank is initially 3/4 full and both pipes are opened simultaneously. How long will it take to empty the tank completely?

18 hours
20 hours
24 hours
16 hours

Explanation: When the waste pipe operates faster than the fill pipe, the net effect is emptying. The waste pipe removes 1/8 of the tank per hour while the fill pipe adds 1/12 per hour. Net emptying rate = 1/8 - 1/12 = 1/24 of the tank per hour. To empty 3/4 of the tank at this rate: (3/4) ÷ (1/24) = 18 hours.

A pipe can fill a tank in 6 hours. Because of a leak, it now takes 9 hours to fill the tank. If the tank is already half full, how long will it take to fill the remaining half with the pipe and leak both active?

6 hours
4 1/2 hours
5 hours
3 3/4 hours

Explanation: The effective filling rate with the leak is 1/9 of the tank per hour (since the full tank takes 9 hours). To fill the remaining half of the tank at this effective rate: (1/2) ÷ (1/9) = 9/2 = 4 1/2 hours.

Pipes A and B can fill a tank in 12 hours and 15 hours respectively, while Pipe C can empty it in 20 hours. All three pipes are opened together. After 4 hours, Pipe C is closed. How much more time is needed to fill the tank completely?

5 hours
3 1/2 hours
4 hours
6 hours

Explanation: With all three pipes open, the net rate is 1/12 + 1/15 - 1/20 = 1/10 of the tank per hour. In 4 hours, 4/10 = 2/5 of the tank is filled. The remaining 3/5 is filled by Pipes A and B together at a rate of 1/12 + 1/15 = 3/20 per hour. Time needed = (3/5) ÷ (3/20) = 4 hours.

Two pipes can fill a tank in 30 minutes and 45 minutes respectively. They are opened together, but the second pipe is turned off 5 minutes before the tank is completely filled. What is the total time taken to fill the tank?

18 minutes
25 minutes
20 minutes
22 minutes

Explanation: Let the total time be t minutes. The first pipe operates for all t minutes, filling t/30 of the tank. The second pipe operates for (t - 5) minutes, filling (t - 5)/45 of the tank. The equation is t/30 + (t - 5)/45 = 1. Multiplying by 90: 3t + 2(t - 5) = 90, which simplifies to 5t = 100, so t = 20 minutes.

Pipe A can fill a tank in 8 hours, Pipe B in 12 hours, and Pipe C can empty it in 16 hours. The tank is initially half full and all three pipes are opened together. How long will it take to fill the tank completely?

3 3/7 hours
4 1/2 hours
5 1/7 hours
2 5/7 hours

Explanation: The net filling rate with all three pipes is 1/8 + 1/12 - 1/16 = 7/48 of the tank per hour. Since the tank is already half full, only 1/2 of the tank remains to be filled. Time required = (1/2) ÷ (7/48) = 24/7 = 3 3/7 hours.

Pipe A can fill a tank in 20 minutes and Pipe B in 30 minutes. Both are opened together, but after 10 minutes Pipe A is closed. What is the total time taken to fill the tank completely?

20 minutes
18 minutes
12 minutes
15 minutes

Explanation: In the first 10 minutes, Pipe A fills 10/20 = 1/2 of the tank and Pipe B fills 10/30 = 1/3 of the tank. Together they fill 5/6 of the tank. The remaining 1/6 is filled by Pipe B alone at 1/30 per minute, requiring (1/6) ÷ (1/30) = 5 minutes. Total time = 10 + 5 = 15 minutes.

A pipe can fill a tank in 10 hours, but due to a leak it takes 12 hours to fill the tank. The tank is initially 2/5 full. If the pipe is opened with the leak present, how long will it take to fill the tank completely?

5 4/5 hours
6 3/5 hours
7 1/5 hours
8 2/5 hours

Explanation: With the leak active, the effective filling rate is 1/12 of the tank per hour. The tank needs 3/5 more to be full. Time required = (3/5) ÷ (1/12) = 36/5 = 7 1/5 hours.

Pipes A and B can fill a tank in 8 hours and 12 hours respectively, while Pipe C can empty it in 24 hours. All three pipes are opened together for 4 hours, after which Pipe A is closed. How long will it take from the start to fill the tank completely?

16 hours
12 hours
10 hours
14 hours

Explanation: With all three pipes open, the net rate is 1/8 + 1/12 - 1/24 = 1/6 of the tank per hour. In 4 hours, 4/6 = 2/3 of the tank is filled. After Pipe A closes, Pipes B and C operate at a net rate of 1/12 - 1/24 = 1/24 per hour. To fill the remaining 1/3: (1/3) ÷ (1/24) = 8 hours. Total time from start = 4 + 8 = 12 hours.

Pipe A can fill a tank in 5 hours and Pipe B in 10 hours. They are opened alternately for 1 hour each, starting with Pipe A. How long will it take to fill the tank completely?

5 3/4 hours
6 1/2 hours
7 hours
8 1/4 hours

Explanation: Each 2-hour cycle consists of Pipe A running for 1 hour (filling 1/5) and Pipe B running for 1 hour (filling 1/10), totaling 3/10 of the tank. After three complete cycles (6 hours), 9/10 of the tank is filled. In the 7th hour, Pipe A operates again and fills the remaining 1/10 at its rate of 1/5 per hour, requiring 1/2 hour. Total time = 6 1/2 hours.

A pipe can fill a tank in 9 hours. Because of a leak, it takes 12 hours to fill the tank. How long would the leak alone take to empty a full tank?

24 hours
42 hours
30 hours
36 hours

Explanation: The pipe's rate is 1/9 of the tank per hour. With the leak, the effective rate is 1/12 per hour. The leak's rate is the difference: 1/9 - 1/12 = 1/36 of the tank per hour. Therefore, the leak alone would empty a full tank in 36 hours.

Pipes A and B can fill a tank in 16 hours and 24 hours respectively, while Pipe C can empty it in 32 hours. If all three pipes are opened together when the tank is empty, how long will it take to fill exactly 3/4 of the tank?

9 3/7 hours
11 1/7 hours
8 4/7 hours
10 2/7 hours

Explanation: The net filling rate with all three pipes is 1/16 + 1/24 - 1/32 = 7/96 of the tank per hour. To fill 3/4 of the tank at this rate: (3/4) ÷ (7/96) = (3/4) × (96/7) = 72/7 = 10 2/7 hours.

Pipe A can fill a tank in 4 hours and Pipe B in 6 hours. Both are opened together, but after 1.5 hours Pipe B is closed. How long will Pipe A take to fill the tank completely from the start?

3 hours
4 hours
2 1/2 hours
3 1/2 hours

Explanation: In 1.5 hours, Pipe A fills 1.5/4 = 3/8 of the tank and Pipe B fills 1.5/6 = 1/4 of the tank. Together they fill 5/8 of the tank. The remaining 3/8 is filled by Pipe A at 1/4 per hour, requiring (3/8) ÷ (1/4) = 1.5 hours. Total time = 1.5 + 1.5 = 3 hours.

A fill pipe can fill a tank in 15 hours and a waste pipe can empty it in 20 hours. The tank is initially 1/3 full. If both pipes are opened together, how long will it take to fill the tank completely?

36 hours
45 hours
40 hours
32 hours

Explanation: The net filling rate is 1/15 - 1/20 = 1/60 of the tank per hour. Since the tank is already 1/3 full, 2/3 of the tank remains to be filled. Time required = (2/3) ÷ (1/60) = 40 hours.

Three pipes A, B, and C can fill a tank in 10 hours, 12 hours, and 15 hours respectively. All three are opened together. After 3 hours, Pipe C is closed. How long will it take from the start to fill the tank completely?

5 1/11 hours
4 4/11 hours
6 2/11 hours
3 8/11 hours

Explanation: With all three pipes open, the combined rate is 1/10 + 1/12 + 1/15 = 1/4 of the tank per hour. In 3 hours, 3/4 of the tank is filled. The remaining 1/4 is filled by Pipes A and B at a rate of 1/10 + 1/12 = 11/60 per hour. Time needed = (1/4) ÷ (11/60) = 15/11 = 1 4/11 hours. Total time = 3 + 1 4/11 = 4 4/11 hours.

Pipe A can fill a tank in 6 hours and Pipe B in 9 hours. Pipe A is opened first and after 2 hours, Pipe B is also opened. How long will it take to fill the tank completely from the start?

5 1/5 hours
6 1/5 hours
4 2/5 hours
3 3/5 hours

Explanation: Pipe A fills 2/6 = 1/3 of the tank in the first 2 hours. The remaining 2/3 is filled by both pipes at a combined rate of 1/6 + 1/9 = 5/18 per hour. Time to fill the remainder = (2/3) ÷ (5/18) = 12/5 = 2 2/5 hours. Total time = 2 + 2 2/5 = 4 2/5 hours.

A pipe can fill a tank in 7 hours. Due to a leak, it takes 10.5 hours to fill the tank. How long would the leak take to empty a full tank?

21 hours
15 hours
24 hours
18 hours

Explanation: The pipe fills at 1/7 of the tank per hour. With the leak, the effective rate is 1/10.5 = 2/21 per hour. The leak's rate is 1/7 - 2/21 = 1/21 of the tank per hour. Thus, the leak alone would empty a full tank in 21 hours.

Pipes A and B can fill a tank in 8 hours and 12 hours respectively, while Pipe C can empty it in 16 hours. All three are opened together. After 4 hours, Pipes B and C are closed. How long will it take from the start to fill the tank completely?

7 1/3 hours
6 2/3 hours
8 1/3 hours
9 hours

Explanation: With all three pipes open, the net rate is 1/8 + 1/12 - 1/16 = 7/48 of the tank per hour. In 4 hours, 28/48 = 7/12 of the tank is filled. The remaining 5/12 is filled by Pipe A alone at 1/8 per hour, requiring (5/12) ÷ (1/8) = 10/3 = 3 1/3 hours. Total time = 4 + 3 1/3 = 7 1/3 hours.

Pipes A and B can fill a tank in 5 hours and 8 hours respectively, while Pipe C can empty it in 10 hours. If all three pipes are opened together, how long will it take to fill exactly 2/3 of the tank?

3 8/27 hours
3 1/9 hours
2 14/27 hours
2 26/27 hours

Explanation: The net filling rate is 1/5 + 1/8 - 1/10 = 9/40 of the tank per hour. To fill 2/3 of the tank at this rate: (2/3) ÷ (9/40) = (2/3) × (40/9) = 80/27 = 2 26/27 hours.

A fill pipe can fill a tank in 14 hours and a waste pipe can empty it in 10 hours. The tank is initially 2/7 full. If both pipes are opened together, how long will it take to empty the tank completely?

8 hours
10 hours
14 hours
12 hours

Explanation: Since the waste pipe operates faster than the fill pipe, the net effect is emptying at a rate of 1/10 - 1/14 = 1/35 of the tank per hour. To empty the initial 2/7 of the tank at this rate: (2/7) ÷ (1/35) = 10 hours.

Pipe A can fill a tank in 6 hours and Pipe B in 10 hours. Both are opened together, but after 3 hours Pipe A is closed. How long will it take to fill the tank completely from the start?

4 1/2 hours
6 hours
5 hours
5 1/2 hours

Explanation: In 3 hours, Pipe A fills 3/6 = 1/2 of the tank and Pipe B fills 3/10 of the tank. Together they fill 4/5 of the tank. The remaining 1/5 is filled by Pipe B at 1/10 per hour, requiring (1/5) ÷ (1/10) = 2 hours. Total time = 3 + 2 = 5 hours.

Pipes A and B can fill a tank in 9 hours and 12 hours respectively, while Pipe C can empty it in 18 hours. If all three pipes are opened together, how long will it take to fill exactly 5/6 of the tank?

5 1/2 hours
7 hours
6 hours
4 3/4 hours

Explanation: The net filling rate is 1/9 + 1/12 - 1/18 = 5/36 of the tank per hour. To fill 5/6 of the tank at this rate: (5/6) ÷ (5/36) = (5/6) × (36/5) = 6 hours.

A pipe can fill a tank in 16 hours. Due to a leak, it takes 20 hours to fill the tank. How long would the leak alone take to empty a full tank?

72 hours
96 hours
64 hours
80 hours

Explanation: The pipe's filling rate is 1/16 of the tank per hour. With the leak, the effective rate is 1/20 per hour. The leak's rate is 1/16 - 1/20 = 1/80 of the tank per hour. Therefore, the leak alone would empty a full tank in 80 hours.

Pipe A can fill a tank in 4 hours and Pipe B in 6 hours. Both are opened together, but after 1 hour Pipe B is closed. How long will it take to fill the tank completely from the start?

3 2/3 hours
4 hours
2 2/3 hours
3 1/3 hours

Explanation: In 1 hour, Pipe A fills 1/4 of the tank and Pipe B fills 1/6 of the tank. Together they fill 5/12 of the tank. The remaining 7/12 is filled by Pipe A at 1/4 per hour, requiring (7/12) ÷ (1/4) = 7/3 = 2 1/3 hours. Total time = 1 + 2 1/3 = 3 1/3 hours.

Pipes A and B can fill a tank in 5 hours and 10 hours respectively, while Pipe C can empty it in 20 hours. All three are opened together for 2 hours, after which Pipe A is closed. How long will it take from the start to fill the tank completely?

14 hours
10 hours
12 hours
16 hours

Explanation: With all three pipes open, the net rate is 1/5 + 1/10 - 1/20 = 1/4 of the tank per hour. In 2 hours, 1/2 of the tank is filled. After Pipe A closes, Pipes B and C operate at a net rate of 1/10 - 1/20 = 1/20 per hour. To fill the remaining 1/2: (1/2) ÷ (1/20) = 10 hours. Total time = 2 + 10 = 12 hours.

Pipe A can fill a tank in 8 hours and Pipe B in 12 hours. Pipe A is opened first and after 3 hours, Pipe B is also opened. How long will it take to fill the tank completely from the start?

5 3/4 hours
5 1/2 hours
6 hours
7 hours

Explanation: Pipe A fills 3/8 of the tank in the first 3 hours. The remaining 5/8 is filled by both pipes at a combined rate of 1/8 + 1/12 = 5/24 per hour. Time to fill the remainder = (5/8) ÷ (5/24) = 3 hours. Total time = 3 + 3 = 6 hours.

A pipe can fill a tank in 18 hours. Due to a leak, it takes 24 hours to fill the tank. How long would the leak alone take to empty a full tank?

84 hours
60 hours
72 hours
48 hours

Explanation: The pipe fills at 1/18 of the tank per hour. With the leak, the effective rate is 1/24 per hour. The leak's rate is 1/18 - 1/24 = 1/72 of the tank per hour. Therefore, the leak alone would empty a full tank in 72 hours.

Two pipes can fill a tank in 20 minutes and 30 minutes respectively, while a third pipe can empty it in 40 minutes. If all three pipes are opened together, how long will it take to fill exactly 3/4 of the tank?

11 3/7 minutes
12 6/7 minutes
15 1/7 minutes
14 2/7 minutes

Explanation: The net filling rate is 1/20 + 1/30 - 1/40 = 7/120 of the tank per minute. To fill 3/4 of the tank at this rate: (3/4) ÷ (7/120) = (3/4) × (120/7) = 90/7 = 12 6/7 minutes.

Pipe A can fill a tank in 5 hours and Pipe B in 7 hours. Both are opened together, but after 2 hours Pipe A is closed. How long will it take to fill the tank completely from the start?

4 1/5 hours
5 1/5 hours
3 4/5 hours
4 3/5 hours

Explanation: In 2 hours, Pipe A fills 2/5 of the tank and Pipe B fills 2/7 of the tank. Together they fill 24/35 of the tank. The remaining 11/35 is filled by Pipe B at 1/7 per hour, requiring (11/35) ÷ (1/7) = 11/5 = 2 1/5 hours. Total time = 2 + 2 1/5 = 4 1/5 hours.

A fill pipe can fill a tank in 12 hours and a waste pipe can empty it in 8 hours. The tank is initially 5/6 full. If both pipes are opened together, how long will it take to empty the tank completely?

20 hours
24 hours
16 hours
18 hours

Explanation: The net emptying rate is 1/8 - 1/12 = 1/24 of the tank per hour. To empty the initial 5/6 of the tank at this rate: (5/6) ÷ (1/24) = 20 hours.

Pipe A can fill a tank in 15 minutes and Pipe B in 25 minutes. Both are opened together, but after 5 minutes Pipe B is closed. How long will it take to fill the tank completely from the start?

15 minutes
10 minutes
14 minutes
12 minutes

Explanation: In 5 minutes, Pipe A fills 5/15 = 1/3 of the tank and Pipe B fills 5/25 = 1/5 of the tank. Together they fill 8/15 of the tank. The remaining 7/15 is filled by Pipe A at 1/15 per minute, requiring (7/15) ÷ (1/15) = 7 minutes. Total time = 5 + 7 = 12 minutes.

Pipes A and B can fill a tank in 6 hours and 9 hours respectively, while Pipe C can empty it in 12 hours. If all three pipes are opened together, how long will it take to fill exactly 5/9 of the tank?

2 6/7 hours
3 3/7 hours
3 1/7 hours
2 4/7 hours

Explanation: The net filling rate is 1/6 + 1/9 - 1/12 = 7/36 of the tank per hour. To fill 5/9 of the tank at this rate: (5/9) ÷ (7/36) = (5/9) × (36/7) = 20/7 = 2 6/7 hours.

A pipe can fill a tank in 10 hours. Due to a leak, it takes 15 hours to fill the tank. How long would the leak alone take to empty a full tank?

30 hours
28 hours
25 hours
35 hours

Explanation: The pipe fills at 1/10 of the tank per hour. With the leak, the effective rate is 1/15 per hour. The leak's rate is 1/10 - 1/15 = 1/30 of the tank per hour. Thus, the leak alone would empty a full tank in 30 hours.

Pipe A can fill a tank in 8 hours and Pipe B in 14 hours. Pipe A is opened first and after 2 hours, Pipe B is also opened. How long will it take to fill the tank completely from the start?

5 1/11 hours
4 8/11 hours
6 2/11 hours
5 9/11 hours

Explanation: Pipe A fills 2/8 = 1/4 of the tank in the first 2 hours. The remaining 3/4 is filled by both pipes at a combined rate of 1/8 + 1/14 = 11/56 per hour. Time to fill the remainder = (3/4) ÷ (11/56) = 42/11 = 3 9/11 hours. Total time = 2 + 3 9/11 = 5 9/11 hours.

Pipes A and B can fill a tank in 10 hours and 15 hours respectively, while Pipe C can empty it in 30 hours. All three are opened together for 5 hours, after which Pipe C is closed. How long will it take from the start to fill the tank completely?

8 hours
7 1/2 hours
6 1/2 hours
7 hours

Explanation: With all three pipes open, the net rate is 1/10 + 1/15 - 1/30 = 2/15 of the tank per hour. In 5 hours, 10/15 = 2/3 of the tank is filled. After Pipe C closes, Pipes A and B operate at a combined rate of 1/10 + 1/15 = 1/6 per hour. To fill the remaining 1/3: (1/3) ÷ (1/6) = 2 hours. Total time = 5 + 2 = 7 hours.

Pipe A can fill a tank in 7 hours and Pipe B in 14 hours. They are opened alternately for 1 hour each, starting with Pipe A. How long will it take to fill the tank completely?

8 3/4 hours
10 hours
8 1/2 hours
9 hours

Explanation: Each 2-hour cycle fills 1/7 + 1/14 = 3/14 of the tank. After four complete cycles (8 hours), 12/14 = 6/7 of the tank is filled. In the 9th hour, Pipe A operates and fills the remaining 1/7 at its rate of 1/7 per hour, requiring exactly 1 hour. Total time = 9 hours.

A fill pipe can fill a tank in 9 hours and a waste pipe can empty it in 12 hours. The tank is initially 1/4 full. If both pipes are opened together, how long will it take to fill the tank completely?

24 hours
32 hours
27 hours
30 hours

Explanation: The net filling rate is 1/9 - 1/12 = 1/36 of the tank per hour. Since the tank is 1/4 full, 3/4 remains to be filled. Time required = (3/4) ÷ (1/36) = 27 hours.

Pipes A and B can fill a tank in 5 hours and 8 hours respectively, while Pipe C can empty it in 16 hours. All three are opened together for 2 hours, after which Pipe A is closed. How long will it take from the start to fill the tank completely?

9 3/5 hours
11 2/5 hours
10 1/5 hours
8 4/5 hours

Explanation: With all three pipes open, the net rate is 1/5 + 1/8 - 1/16 = 21/80 of the tank per hour. In 2 hours, 42/80 = 21/40 of the tank is filled. After Pipe A closes, Pipes B and C operate at a net rate of 1/8 - 1/16 = 1/16 per hour. To fill the remaining 19/40: (19/40) ÷ (1/16) = 38/5 = 7 3/5 hours. Total time = 2 + 7 3/5 = 9 3/5 hours.

Pipe A can fill a tank in 12 hours and Pipe B in 18 hours. Both are opened together, but after 4 hours Pipe A is closed. How long will it take to fill the tank completely from the start?

11 hours
14 hours
10 hours
12 hours

Explanation: In 4 hours, Pipe A fills 4/12 = 1/3 of the tank and Pipe B fills 4/18 = 2/9 of the tank. Together they fill 5/9 of the tank. The remaining 4/9 is filled by Pipe B at 1/18 per hour, requiring (4/9) ÷ (1/18) = 8 hours. Total time = 4 + 8 = 12 hours.

Pipes A and B can fill a tank in 6 hours and 10 hours respectively, while Pipe C can empty it in 15 hours. If all three pipes are opened together, how long will it take to fill exactly 4/5 of the tank?

3 1/2 hours
4 1/2 hours
4 hours
5 hours

Explanation: The net filling rate is 1/6 + 1/10 - 1/15 = 1/5 of the tank per hour. To fill 4/5 of the tank at this rate: (4/5) ÷ (1/5) = 4 hours.

A pipe can fill a tank in 20 hours. Due to a leak, it takes 25 hours to fill the tank. How long would the leak alone take to empty a full tank?

90 hours
100 hours
80 hours
110 hours

Explanation: The pipe fills at 1/20 of the tank per hour. With the leak, the effective rate is 1/25 per hour. The leak's rate is 1/20 - 1/25 = 1/100 of the tank per hour. Therefore, the leak alone would empty a full tank in 100 hours.

Pipes A and B can fill a tank in 4 hours and 6 hours respectively, while Pipe C can empty it in 12 hours. All three are opened together for 2 hours, after which Pipe C is closed. How long will it take from the start to fill the tank completely?

2 4/5 hours
3 1/5 hours
3 3/5 hours
2 2/5 hours

Explanation: With all three pipes open, the net rate is 1/4 + 1/6 - 1/12 = 1/3 of the tank per hour. In 2 hours, 2/3 of the tank is filled. After Pipe C closes, Pipes A and B operate at a combined rate of 1/4 + 1/6 = 5/12 per hour. To fill the remaining 1/3: (1/3) ÷ (5/12) = 4/5 hours. Total time = 2 + 4/5 = 2 4/5 hours.

A fill pipe can fill a tank in 10 hours and a waste pipe can empty it in 6 hours. The tank is initially 2/3 full. If both pipes are opened together, how long will it take to empty the tank completely?

8 hours
15 hours
10 hours
12 hours

Explanation: Since the waste pipe operates faster than the fill pipe, the net effect is emptying at a rate of 1/6 - 1/10 = 1/15 of the tank per hour. To empty the initial 2/3 of the tank at this rate: (2/3) ÷ (1/15) = 10 hours.

Pipe A can fill a tank in 8 hours and Pipe B in 16 hours. Both are opened together, but after 2 hours Pipe B is closed. How long will it take to fill the tank completely from the start?

6 hours
7 hours
5 1/2 hours
8 hours

Explanation: In 2 hours, Pipe A fills 2/8 = 1/4 of the tank and Pipe B fills 2/16 = 1/8 of the tank. Together they fill 3/8 of the tank. The remaining 5/8 is filled by Pipe A at 1/8 per hour, requiring (5/8) ÷ (1/8) = 5 hours. Total time = 2 + 5 = 7 hours.

Pipes A and B can fill a tank in 7 hours and 14 hours respectively, while Pipe C can empty it in 21 hours. If all three pipes are opened together, how long will it take to fill exactly 5/7 of the tank?

5 1/7 hours
4 5/7 hours
4 2/7 hours
3 5/7 hours

Explanation: The net filling rate is 1/7 + 1/14 - 1/21 = 1/6 of the tank per hour. To fill 5/7 of the tank at this rate: (5/7) ÷ (1/6) = 30/7 = 4 2/7 hours.

A pipe can fill a tank in 12 hours. Due to a leak, it takes 18 hours to fill the tank. How long would the leak alone take to empty a full tank?

30 hours
36 hours
42 hours
24 hours

Explanation: The pipe fills at 1/12 of the tank per hour. With the leak, the effective rate is 1/18 per hour. The leak's rate is 1/12 - 1/18 = 1/36 of the tank per hour. Thus, the leak alone would empty a full tank in 36 hours.

Pipe A can fill a tank in 5 hours and Pipe B in 10 hours. Both are opened together, but after 2 hours Pipe A is closed. How long will it take to fill the tank completely from the start?

7 hours
6 hours
4 1/2 hours
5 hours

Explanation: In 2 hours, Pipe A fills 2/5 of the tank and Pipe B fills 2/10 = 1/5 of the tank. Together they fill 3/5 of the tank. The remaining 2/5 is filled by Pipe B at 1/10 per hour, requiring (2/5) ÷ (1/10) = 4 hours. Total time = 2 + 4 = 6 hours.

Pipes A and B can fill a tank in 6 hours and 8 hours respectively, while Pipe C can empty it in 12 hours. All three are opened together for 3 hours, after which Pipe B is closed. How long will it take from the start to fill the tank completely?

8 hours
6 3/4 hours
8 1/2 hours
7 1/2 hours

Explanation: With all three pipes open, the net rate is 1/6 + 1/8 - 1/12 = 5/24 of the tank per hour. In 3 hours, 15/24 = 5/8 of the tank is filled. After Pipe B closes, Pipes A and C operate at a net rate of 1/6 - 1/12 = 1/12 per hour. To fill the remaining 3/8: (3/8) ÷ (1/12) = 9/2 = 4 1/2 hours. Total time = 3 + 4 1/2 = 7 1/2 hours.

Pipe A can fill a tank in 9 hours and Pipe B in 15 hours. Pipe A is opened first and after 3 hours, Pipe B is also opened. How long will it take to fill the tank completely from the start?

7 1/4 hours
6 3/4 hours
6 1/4 hours
5 3/4 hours

Explanation: Pipe A fills 3/9 = 1/3 of the tank in the first 3 hours. The remaining 2/3 is filled by both pipes at a combined rate of 1/9 + 1/15 = 8/45 per hour. Time to fill the remainder = (2/3) ÷ (8/45) = 15/4 = 3 3/4 hours. Total time = 3 + 3 3/4 = 6 3/4 hours.

Pipes A and B can fill a tank in 10 hours and 20 hours respectively, while Pipe C can empty it in 30 hours. If all three pipes are opened together, how long will it take to fill exactly 7/10 of the tank?

5 1/2 hours
7 hours
4 3/4 hours
6 hours

Explanation: The net filling rate is 1/10 + 1/20 - 1/30 = 7/60 of the tank per hour. To fill 7/10 of the tank at this rate: (7/10) ÷ (7/60) = 6 hours.

A pipe can fill a tank in 14 hours. Due to a leak, it takes 21 hours to fill the tank. How long would the leak alone take to empty a full tank?

42 hours
35 hours
48 hours
36 hours

Explanation: The pipe fills at 1/14 of the tank per hour. With the leak, the effective rate is 1/21 per hour. The leak's rate is 1/14 - 1/21 = 1/42 of the tank per hour. Therefore, the leak alone would empty a full tank in 42 hours.

Pipes A and B can fill a tank in 6 hours and 9 hours respectively, while Pipe C can empty it in 18 hours. All three are opened together for 2 hours, after which Pipe A is closed. How long will it take from the start to fill the tank completely?

11 hours
12 hours
10 hours
14 hours

Explanation: With all three pipes open, the net rate is 1/6 + 1/9 - 1/18 = 2/9 of the tank per hour. In 2 hours, 4/9 of the tank is filled. After Pipe A closes, Pipes B and C operate at a net rate of 1/9 - 1/18 = 1/18 per hour. To fill the remaining 5/9: (5/9) ÷ (1/18) = 10 hours. Total time = 2 + 10 = 12 hours.

Pipe A can fill a tank in 4 hours and Pipe B in 10 hours. Both are opened together, but after 1 hour Pipe B is closed. How long will it take to fill the tank completely from the start?

2 4/5 hours
3 3/5 hours
3 1/5 hours
4 hours

Explanation: In 1 hour, Pipe A fills 1/4 of the tank and Pipe B fills 1/10 of the tank. Together they fill 7/20 of the tank. The remaining 13/20 is filled by Pipe A at 1/4 per hour, requiring (13/20) ÷ (1/4) = 13/5 = 2 3/5 hours. Total time = 1 + 2 3/5 = 3 3/5 hours.

A fill pipe can fill a tank in 15 hours and a waste pipe can empty it in 20 hours. The tank is initially 3/5 full. If both pipes are opened together, how long will it take to fill the tank completely?

24 hours
28 hours
20 hours
18 hours

Explanation: The net filling rate is 1/15 - 1/20 = 1/60 of the tank per hour. Since the tank is 3/5 full, 2/5 remains to be filled. Time required = (2/5) ÷ (1/60) = 24 hours.

Pipes A and B can fill a tank in 8 hours and 12 hours respectively, while Pipe C can empty it in 4 hours. If all three pipes are opened together when the tank is full, how long will it take to empty the tank completely?

24 hours
20 hours
16 hours
18 hours

Explanation: Since the emptying pipe operates faster than the combined filling rate, the net effect is emptying. The net rate is 1/4 - 1/8 - 1/12 = 1/24 of the tank per hour. To empty a full tank at this rate: 1 ÷ (1/24) = 24 hours.

Pipes And Cisterns Practice

Performance Summary

Choose a Topic to Start Practice

Daily Current Affairs