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A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?
- a)5 minutes
- b)4 minutes
- c)6 minutes
- d)8 minutes
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and ...
pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15
1/15 : 2/5 :: 1: x
2/5 * 15 = 6 minutes.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15
1/15 : 2/5 :: 1: x
2/5 * 15 = 6 minutes.
Most Upvoted Answer
A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and ...
pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15
1/15 : 2/5 :: 1: x
2/5 * 15 = 6 minutes.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15
1/15 : 2/5 :: 1: x
2/5 * 15 = 6 minutes.
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Community Answer
A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and ...
Given Information
- The cistern is two-fifth full.
- Pipe A can fill a tank in 10 minutes.
- Pipe B can empty the same tank in 6 minutes.
To Find:
- The time taken to empty/fill the tank completely when both pipes are open.
Approach:
- Let's assume that the capacity of the tank is 10 liters.
- As per the question, the cistern is two-fifth full, which means it contains 4 liters of water (2/5 * 10).
- Now, we need to find out the net flow rate of water when both pipes are open.
- Pipe A can fill the tank in 10 minutes, which means it can fill 1 liter in 1 minute.
- Pipe B can empty the same tank in 6 minutes, which means it can empty 1.67 liters (10/6) in 1 minute.
- Therefore, the net flow rate of water when both pipes are open = (1 - 1.67) = -0.67 liters/minute.
- The negative sign indicates that the water is being emptied from the tank.
Calculation:
- To empty the remaining 4 liters of water from the cistern, it will take 4/0.67 = 5.97 minutes.
- Therefore, the time taken to empty/fill the tank completely when both pipes are open is approximately 6 minutes.
Hence, the correct answer is option (c) 6 minutes.
- The cistern is two-fifth full.
- Pipe A can fill a tank in 10 minutes.
- Pipe B can empty the same tank in 6 minutes.
To Find:
- The time taken to empty/fill the tank completely when both pipes are open.
Approach:
- Let's assume that the capacity of the tank is 10 liters.
- As per the question, the cistern is two-fifth full, which means it contains 4 liters of water (2/5 * 10).
- Now, we need to find out the net flow rate of water when both pipes are open.
- Pipe A can fill the tank in 10 minutes, which means it can fill 1 liter in 1 minute.
- Pipe B can empty the same tank in 6 minutes, which means it can empty 1.67 liters (10/6) in 1 minute.
- Therefore, the net flow rate of water when both pipes are open = (1 - 1.67) = -0.67 liters/minute.
- The negative sign indicates that the water is being emptied from the tank.
Calculation:
- To empty the remaining 4 liters of water from the cistern, it will take 4/0.67 = 5.97 minutes.
- Therefore, the time taken to empty/fill the tank completely when both pipes are open is approximately 6 minutes.
Hence, the correct answer is option (c) 6 minutes.
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A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?a)5 minutesb)4 minutesc)6 minutesd)8 minutese)None of the AboveCorrect answer is option 'C'. Can you explain this answer?
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