FPSC (Federal Public Service Commission) · CSS (Central Superior Services)
Pipes and Cisterns set-1
Pipes and Cisterns
· Mathematics/General Ability
200 MCQs
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1–20
of 200 MCQs
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1
Pipe A can fill a tank in 10 hours and Pipe B can fill it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
Answer:
6 hours
Step 1: Determine the hourly rate of each pipe. Pipe A fills 1/10 of the tank per hour, and Pipe B fills 1/15 of the tank per hour. Step 2: Calculate their combined hourly rate by adding individual rates: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Step 3: Since together they fill 1/6 of the tank in one hour, they will take exactly 6 hours to fill the entire tank.
2
Two pipes can fill a cistern in 20 hours and 30 hours respectively. If both are opened simultaneously, find the time taken to fill the cistern.
Answer:
12 hours
Step 1: The first pipe's filling rate is 1/20 per hour. The second pipe's filling rate is 1/30 per hour. Step 2: Combine their rates to find the total work done per hour: 1/20 + 1/30. The least common multiple (LCM) is 60. So, 3/60 + 2/60 = 5/60 = 1/12. Step 3: The reciprocal of the combined rate gives the total time. Thus, it takes 12 hours to fill the cistern.
3
A pipe can fill a pool in 4 hours, and another pipe can fill it in 12 hours. How long will it take to fill the pool if both are used together?
Answer:
3 hours
Step 1: Calculate the work rate of each pipe. Pipe 1 = 1/4 per hour, Pipe 2 = 1/12 per hour. Step 2: Add the rates to find the joint efficiency: 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3. Step 3: A combined rate of 1/3 means the entire pool will be filled in 3 hours.
4
Pipe A fills a tank in 12 hours and Pipe B fills the same tank in 24 hours. Working together, in how many hours will the tank be full?
Answer:
8 hours
Step 1: Find the fraction of the tank filled by each pipe in one hour: Pipe A = 1/12, Pipe B = 1/24. Step 2: Sum these fractions to find the combined hourly rate: 1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8. Step 3: Invert the fraction 1/8 to find the total time required, which is exactly 8 hours.
5
If Pipe X can fill a tank in 15 minutes and Pipe Y can fill it in 20 minutes, how much time will it take if both operate together?
Answer:
8 4/7 minutes
Step 1: Identify the per-minute work rate of each pipe: Pipe X = 1/15, Pipe Y = 1/20. Step 2: Add the rates together using a common denominator of 60: 4/60 + 3/60 = 7/60. Step 3: The time taken is the reciprocal of 7/60, which is 60/7 minutes. Converting this to a mixed fraction yields 8 4/7 minutes.
6
Pipe A can fill a reservoir in 5 hours and Pipe B can fill it in 20 hours. How long will it take to fill the reservoir together?
Answer:
4 hours
Step 1: Formulate the hourly rates: 1/5 for Pipe A and 1/20 for Pipe B. Step 2: Add the rates: 1/5 + 1/20 = 4/20 + 1/20 = 5/20. Simplify the fraction to 1/4. Step 3: Since the combined rate is 1/4 of the reservoir per hour, the total time to fill it is 4 hours.
7
Two pipes can fill a tank in 8 hours and 24 hours respectively. If they are opened simultaneously, what is the time taken to fill the tank?
Answer:
6 hours
Step 1: Establish the individual work rates. Pipe 1 fills at 1/8 per hour, and Pipe 2 fills at 1/24 per hour. Step 2: Calculate the combined work rate by adding the fractions: 1/8 + 1/24 = 3/24 + 1/24 = 4/24 = 1/6. Step 3: The reciprocal of the combined rate is 6, meaning the tank will be full in 6 hours.
8
Pipe P can fill a tub in 10 minutes, and Pipe Q can fill it in 40 minutes. Working together, what is the total time required?
Answer:
8 minutes
Step 1: Write down the per-minute filling rates for both pipes: P = 1/10 and Q = 1/40. Step 2: Find the combined rate by adding the two fractions together: 1/10 + 1/40 = 4/40 + 1/40 = 5/40 = 1/8. Step 3: The total time is the reciprocal of the combined rate, which equals 8 minutes.
9
A pipe can fill a water tank in 18 hours and a second pipe can fill it in 36 hours. If both pipes are opened, the tank will be filled in:
Answer:
12 hours
Step 1: The rate of the first pipe is 1/18, and the second pipe's rate is 1/36. Step 2: Add these rates to find the overall filling speed: 1/18 + 1/36 = 2/36 + 1/36 = 3/36. Step 3: Simplify 3/36 to 1/12. Therefore, both pipes working together will fill the tank in 12 hours.
10
Pipe M fills a tank in 6 hours, while Pipe N fills the same tank in 8 hours. How long will it take for both to fill the tank together?
Answer:
3.42 hours
Step 1: Combine their hourly rates. Rate of M = 1/6, Rate of N = 1/8. Step 2: Total rate = 1/6 + 1/8 = 4/24 + 3/24 = 7/24. Step 3: The total time is 24/7 hours. Since 24 divided by 7 is approximately 3.428 hours, 3.42 hours is the correct choice.
11
Pipe A fills a tank in 10 hours, while Pipe B can empty the full tank in 15 hours. If both are opened together, how long will it take to fill the tank?
Answer:
30 hours
Step 1: Identify the nature of the pipes. A is an inlet (positive rate = 1/10) and B is an outlet (negative rate = -1/15). Step 2: Calculate the net filling rate: 1/10 - 1/15. The LCM is 30, so 3/30 - 2/30 = 1/30. Step 3: A net rate of +1/30 means the tank fills at a rate of 1/30th per hour. Total time required is 30 hours.
12
A cistern can be filled by an inlet pipe in 8 hours and emptied by an outlet pipe in 12 hours. If both are opened, find the time to fill the cistern.
Answer:
24 hours
Step 1: The inlet pipe fills 1/8 of the cistern per hour. The outlet pipe empties 1/12 of the cistern per hour. Step 2: The net hourly work is 1/8 - 1/12 = 3/24 - 2/24 = 1/24. Step 3: Because the net work is positive, the cistern is filling. It will take exactly 24 hours to become full.
13
An inlet pipe fills a tank in 5 hours. An outlet pipe empties it in 10 hours. If both pipes are opened simultaneously, when will the tank be full?
Answer:
10 hours
Step 1: Determine the rates: Fill rate = 1/5 per hour, Empty rate = -1/10 per hour. Step 2: Calculate the effective filling rate: 1/5 - 1/10 = 2/10 - 1/10 = 1/10. Step 3: Since the effective rate is 1/10 of the tank per hour, the entire tank will be filled in 10 hours.
14
A pipe can fill a drum in 20 minutes, but a drain can empty the full drum in 30 minutes. If both are left open, how long will it take to fill the drum?
Answer:
60 minutes
Step 1: Convert the times to per-minute rates. Inlet rate = 1/20, Outlet rate = 1/30. Step 2: Find the net rate per minute: 1/20 - 1/30 = 3/60 - 2/60 = 1/60. Step 3: The net rate is 1/60 per minute. This means it will take exactly 60 minutes (or 1 hour) to fill the drum.
15
Pipe X fills a tank in 12 hours. Pipe Y empties the full tank in 18 hours. If both are opened, what is the total time taken to fill the tank?
Answer:
36 hours
Step 1: Identify rates. Filling rate is 1/12, and emptying rate is -1/18. Step 2: The net filling rate per hour is 1/12 - 1/18 = 3/36 - 2/36 = 1/36. Step 3: The reciprocal of the net rate gives the time. Thus, it will take 36 hours to completely fill the tank.
16
A tap fills a cistern in 15 hours. Due to a leak at the bottom, it takes 25 hours to fill. In what time will the leak alone empty the full cistern?
Answer:
37.5 hours
Step 1: The normal filling rate is 1/15. The effective rate with the leak is 1/25. Let the leak's emptying rate be 1/x. Step 2: Form the equation: 1/15 - 1/x = 1/25. Step 3: Solve for 1/x: 1/x = 1/15 - 1/25 = 5/75 - 3/75 = 2/75. The time taken by the leak alone is 75/2 = 37.5 hours.
17
Pipe A fills a pool in 6 hours. Pipe B can empty the full pool in 9 hours. If both run simultaneously, how many hours will it take to fill the pool?
Answer:
18 hours
Step 1: Pipe A's rate is 1/6 per hour. Pipe B's rate is -1/9 per hour. Step 2: Combine the rates: 1/6 - 1/9 = 3/18 - 2/18 = 1/18. Step 3: The overall net rate is 1/18 of the pool per hour. Therefore, it will take 18 hours to completely fill the pool.
18
A cistern has a filling pipe taking 4 hours and an emptying pipe taking 6 hours. If both are opened, how long to fill the empty cistern?
Answer:
12 hours
Step 1: Filling rate is 1/4. Emptying rate is 1/6. Step 2: Find the net hourly rate: 1/4 - 1/6 = 3/12 - 2/12 = 1/12. Step 3: Since 1/12 of the cistern fills every hour, the total time required to fill it is 12 hours.
19
Pipe 1 can fill a tank in 10 hours. Pipe 2 can empty it in 20 hours. What is the time required to fill the tank if both are opened?
Answer:
20 hours
Step 1: Define the rates: Pipe 1 = +1/10, Pipe 2 = -1/20. Step 2: Calculate the net rate: 1/10 - 1/20 = 2/20 - 1/20 = 1/20. Step 3: The positive fraction indicates the tank is filling at a rate of 1/20 per hour. It will take 20 hours to fill.
20
A filling pipe takes 24 hours to fill a tank, while an emptying pipe takes 36 hours to empty it. When both are open, how long will it take to fill the tank?
Answer:
72 hours
Step 1: The rate of filling is 1/24 per hour. The rate of emptying is 1/36 per hour. Step 2: Calculate the combined net rate: 1/24 - 1/36 = 3/72 - 2/72 = 1/72. Step 3: The reciprocal of 1/72 represents the total time. Thus, it will take exactly 72 hours to fill the tank.
