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Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _________.
- a)16.50
- b)14.50
- c)15.50
- d)13.50
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively,...
1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours =
Tank filled by when Q and R works for another 6 hours =
Total tank filled in these 10 hours =
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in 9 hours)
Therefore, total time required to fill the tank =4 + 6 + 4.5 = 14.5 hours
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours =
Tank filled by when Q and R works for another 6 hours =
Total tank filled in these 10 hours =
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in 9 hours)
Therefore, total time required to fill the tank =4 + 6 + 4.5 = 14.5 hours
Most Upvoted Answer
Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively,...
Solution:
Let's calculate the fill rate of each pipe first:
Pipe P can fill the tank in 6 hours, so its fill rate is 1/6 of the tank per hour.
Pipe Q can fill the tank in 9 hours, so its fill rate is 1/9 of the tank per hour.
Pipe R can empty the tank in 12 hours, so its emptying rate is 1/12 of the tank per hour.
Now, let's analyze the given information step by step:
1. Initially, P and R are open for 4 hours.
- Pipe P fills the tank at a rate of 1/6 of the tank per hour for 4 hours, so it fills 4/6 of the tank.
- Pipe R empties the tank at a rate of 1/12 of the tank per hour for 4 hours, so it empties 4/12 of the tank.
2. Then P is closed and Q is opened.
- Pipe Q fills the remaining tank, which is (1 - 4/6 - 4/12) = 1/6 of the tank.
- Pipe Q fills the tank at a rate of 1/9 of the tank per hour for 6 hours, so it fills 6/9 of the tank.
3. After 6 more hours, R is closed.
- Pipe Q continues to fill the tank for 6 more hours, filling another 6/9 of the tank.
Now, let's calculate the total amount of the tank filled:
- Total amount filled = 4/6 + 4/12 + 1/6 + 6/9 + 6/9
= 2/3 + 1/3 + 1/6 + 2/3 + 2/3
= 4/3 + 1/6 + 4/3
= 8/6 + 1/6 + 4/3
= 9/6 + 4/3
= 3/2 + 4/3
= (9 + 8)/6
= 17/6
To find the total time taken to fill the tank, we need to invert the fill rate and multiply it by the total amount filled:
- Total time taken = (6/1) * (17/6)
= 17/1
= 17 hours
Therefore, the total time taken to fill the tank is 17 hours, which is equivalent to 17 hours and 30 minutes.
So, the correct answer is option B) 14.50 hours.
Let's calculate the fill rate of each pipe first:
Pipe P can fill the tank in 6 hours, so its fill rate is 1/6 of the tank per hour.
Pipe Q can fill the tank in 9 hours, so its fill rate is 1/9 of the tank per hour.
Pipe R can empty the tank in 12 hours, so its emptying rate is 1/12 of the tank per hour.
Now, let's analyze the given information step by step:
1. Initially, P and R are open for 4 hours.
- Pipe P fills the tank at a rate of 1/6 of the tank per hour for 4 hours, so it fills 4/6 of the tank.
- Pipe R empties the tank at a rate of 1/12 of the tank per hour for 4 hours, so it empties 4/12 of the tank.
2. Then P is closed and Q is opened.
- Pipe Q fills the remaining tank, which is (1 - 4/6 - 4/12) = 1/6 of the tank.
- Pipe Q fills the tank at a rate of 1/9 of the tank per hour for 6 hours, so it fills 6/9 of the tank.
3. After 6 more hours, R is closed.
- Pipe Q continues to fill the tank for 6 more hours, filling another 6/9 of the tank.
Now, let's calculate the total amount of the tank filled:
- Total amount filled = 4/6 + 4/12 + 1/6 + 6/9 + 6/9
= 2/3 + 1/3 + 1/6 + 2/3 + 2/3
= 4/3 + 1/6 + 4/3
= 8/6 + 1/6 + 4/3
= 9/6 + 4/3
= 3/2 + 4/3
= (9 + 8)/6
= 17/6
To find the total time taken to fill the tank, we need to invert the fill rate and multiply it by the total amount filled:
- Total time taken = (6/1) * (17/6)
= 17/1
= 17 hours
Therefore, the total time taken to fill the tank is 17 hours, which is equivalent to 17 hours and 30 minutes.
So, the correct answer is option B) 14.50 hours.
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Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _________.a)16.50b)14.50c)15.50d)13.50Correct answer is option 'B'. Can you explain this answer?
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