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Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed, In how much time, will the tank be full?
- a)12 hrs
- b)13 hrs
- c)16 hrs
- d)18 hrs
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a tank in 15 hours and 20 hours respectivel...
Most Upvoted Answer
Two pipes A and B can fill a tank in 15 hours and 20 hours respectivel...
Given:
- Pipe A fills the tank in 15 hours.
- Pipe B fills the tank in 20 hours.
- Pipe C empties the tank in 25 hours.
- All pipes are opened in the beginning.
- After 10 hours, pipe C is closed.
To determine the time it takes to fill the tank, we need to find the rate at which each pipe fills or empties the tank.
- The rate at which pipe A fills the tank is 1/15 tank/hour.
- The rate at which pipe B fills the tank is 1/20 tank/hour.
- The rate at which pipe C empties the tank is -1/25 tank/hour (negative because it empties the tank).
When all pipes are opened, the net rate at which the tank is filled is:
1/15 + 1/20 - 1/25 = 1/12 tank/hour
This means that the tank fills at a rate of 1/12 tank per hour when all pipes are opened.
After 10 hours, pipe C is closed. In those 10 hours, the tank was being filled at a rate of:
10(1/12) = 5/6 tank
Therefore, the amount of empty space left in the tank is:
1 - 5/6 = 1/6 tank
To fill this remaining space, we need to use pipes A and B only. The net rate at which the tank is filled now is:
1/15 + 1/20 = 7/60 tank/hour
Using the formula:
time = amount of work / rate
We can find the time it takes to fill the remaining space:
time = (1/6) / (7/60) = 12 hours
Therefore, the total time it takes to fill the tank is:
10 + 12 = 22 hours
But the question asks for the time it takes to fill the tank AFTER pipe C is closed. So the answer is:
10 + 12 - 10 = 12 hours
Therefore, the correct answer is option A (12 hours).
- Pipe A fills the tank in 15 hours.
- Pipe B fills the tank in 20 hours.
- Pipe C empties the tank in 25 hours.
- All pipes are opened in the beginning.
- After 10 hours, pipe C is closed.
To determine the time it takes to fill the tank, we need to find the rate at which each pipe fills or empties the tank.
- The rate at which pipe A fills the tank is 1/15 tank/hour.
- The rate at which pipe B fills the tank is 1/20 tank/hour.
- The rate at which pipe C empties the tank is -1/25 tank/hour (negative because it empties the tank).
When all pipes are opened, the net rate at which the tank is filled is:
1/15 + 1/20 - 1/25 = 1/12 tank/hour
This means that the tank fills at a rate of 1/12 tank per hour when all pipes are opened.
After 10 hours, pipe C is closed. In those 10 hours, the tank was being filled at a rate of:
10(1/12) = 5/6 tank
Therefore, the amount of empty space left in the tank is:
1 - 5/6 = 1/6 tank
To fill this remaining space, we need to use pipes A and B only. The net rate at which the tank is filled now is:
1/15 + 1/20 = 7/60 tank/hour
Using the formula:
time = amount of work / rate
We can find the time it takes to fill the remaining space:
time = (1/6) / (7/60) = 12 hours
Therefore, the total time it takes to fill the tank is:
10 + 12 = 22 hours
But the question asks for the time it takes to fill the tank AFTER pipe C is closed. So the answer is:
10 + 12 - 10 = 12 hours
Therefore, the correct answer is option A (12 hours).
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Community Answer
Two pipes A and B can fill a tank in 15 hours and 20 hours respectivel...
Part of tank filled in 1hr by A= 1/15
B= 1/20
emptied C= 1/25
let x be more time to fill the tank
10(1/15 + 1/20 - 1/25) + (1/15 + 1/20)*x =1
x = 2
total time =10+2 = 12
B= 1/20
emptied C= 1/25
let x be more time to fill the tank
10(1/15 + 1/20 - 1/25) + (1/15 + 1/20)*x =1
x = 2
total time =10+2 = 12
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