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A water tank is 2/5 th full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
- a)6 min to empty
- b)7 min to full
- c)6 min to full
- d)7 min to empty
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A water tank is 2/5 th full. Pipe A can fill a tank in 10 minutes and...
Solution:
Given, the water tank is 2/5 th full.
Let the capacity of the tank be 5 units.
Then, the tank is filled with 2 units of water.
Pipe A can fill the tank in 10 minutes.
Therefore, the rate at which pipe A can fill the tank = 1/10 units per minute.
Pipe B can empty the tank in 6 minutes.
Therefore, the rate at which pipe B can empty the tank = 1/6 units per minute.
Let's consider the case when both pipes A and B are open.
Case 1: Tank is filled completely
Let the time taken to fill the tank completely be 't' minutes.
Then, the total amount of water filled in 't' minutes is equal to the capacity of the tank, which is 5 units.
Hence, we can write the equation as:
(1/10 - 1/6) t = 5
Simplifying the above equation, we get:
t = 30 minutes
Therefore, it takes 30 minutes to fill the tank completely when both pipes A and B are open.
Case 2: Tank is emptied completely
Let the time taken to empty the tank completely be 't' minutes.
Then, the total amount of water emptied in 't' minutes is equal to the initial amount of water in the tank, which is 2 units.
Hence, we can write the equation as:
(-1/6 - 1/10) t = 2
Simplifying the above equation, we get:
t = 6 minutes
Therefore, it takes 6 minutes to empty the tank completely when both pipes A and B are open.
Conclusion:
Hence, the correct answer is option 'A' - 6 min to empty.
Given, the water tank is 2/5 th full.
Let the capacity of the tank be 5 units.
Then, the tank is filled with 2 units of water.
Pipe A can fill the tank in 10 minutes.
Therefore, the rate at which pipe A can fill the tank = 1/10 units per minute.
Pipe B can empty the tank in 6 minutes.
Therefore, the rate at which pipe B can empty the tank = 1/6 units per minute.
Let's consider the case when both pipes A and B are open.
Case 1: Tank is filled completely
Let the time taken to fill the tank completely be 't' minutes.
Then, the total amount of water filled in 't' minutes is equal to the capacity of the tank, which is 5 units.
Hence, we can write the equation as:
(1/10 - 1/6) t = 5
Simplifying the above equation, we get:
t = 30 minutes
Therefore, it takes 30 minutes to fill the tank completely when both pipes A and B are open.
Case 2: Tank is emptied completely
Let the time taken to empty the tank completely be 't' minutes.
Then, the total amount of water emptied in 't' minutes is equal to the initial amount of water in the tank, which is 2 units.
Hence, we can write the equation as:
(-1/6 - 1/10) t = 2
Simplifying the above equation, we get:
t = 6 minutes
Therefore, it takes 6 minutes to empty the tank completely when both pipes A and B are open.
Conclusion:
Hence, the correct answer is option 'A' - 6 min to empty.
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Community Answer
A water tank is 2/5 th full. Pipe A can fill a tank in 10 minutes and...
- Since pipe B is faster than pipe A and thus, the tank will be emptied.
- Part of the tank to be emptied = 2/5
- Part emptied by (A+B) in 1 minute= (1/6 - 1/10) = 1/15.
Therefore,
⇒ 1/15 : 2/5 :: 1: x
⇒ 2/5 * 15 = 6 minutes
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A water tank is 2/5 th full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?a)6 min to emptyb)7 min to fullc)6 min to fulld)7 min to emptyCorrect answer is option 'A'. Can you explain this answer?
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