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Two pipes P and Q can fill a tank in 36 and 24 minutes respectively. If both the pipes are opened simultaneously, after how much time pipe Q should be closed so that tank is full in 30 minutes.
- a)2min
- b)4min
- c)6min
- d)8min
- e)None of these
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 36 and 24 minutes respectively. I...
Let after T time, Q is closed, (1/36 + 1/24)*T + (1/36)*(30 – T) = 1
Most Upvoted Answer
Two pipes P and Q can fill a tank in 36 and 24 minutes respectively. I...
To solve this problem, we need to determine the rate at which each pipe fills the tank, and then calculate how long it would take for both pipes to fill the tank if they were left open for 30 minutes. We can then subtract the time it would take for Pipe Q to fill the remaining portion of the tank in order to determine when it should be closed.
1. Determine the rate of filling for each pipe:
- Pipe P fills the tank in 36 minutes, so its filling rate is 1/36 of the tank per minute.
- Pipe Q fills the tank in 24 minutes, so its filling rate is 1/24 of the tank per minute.
2. Calculate the combined filling rate for both pipes:
- When both pipes are open, their combined filling rate is the sum of their individual rates: 1/36 + 1/24 = 3/72 + 4/72 = 7/72 of the tank per minute.
3. Calculate the time it would take for both pipes to fill the tank in 30 minutes:
- Since the combined filling rate is 7/72 of the tank per minute, the time it would take for both pipes to fill the tank in 30 minutes can be calculated as follows:
- Let x be the fraction of the tank filled in 30 minutes.
- We can set up the equation: x = (7/72) * 30.
- Solving for x, we find that the tank would be filled to 7/24 in 30 minutes.
4. Determine how long Pipe Q should be open:
- Since we want the tank to be completely full in 30 minutes, we subtract the fraction of the tank remaining to be filled by Pipe Q from 1.
- 1 - 7/24 = 17/24.
- The time it would take for Pipe Q to fill the remaining 17/24 of the tank can be calculated as follows:
- Let t be the time in minutes.
- We can set up the equation: (1/24) * t = 17/24.
- Solving for t, we find that Pipe Q should be closed after 17 minutes.
Therefore, Pipe Q should be closed after 17 minutes in order to fill the tank in a total of 30 minutes.
1. Determine the rate of filling for each pipe:
- Pipe P fills the tank in 36 minutes, so its filling rate is 1/36 of the tank per minute.
- Pipe Q fills the tank in 24 minutes, so its filling rate is 1/24 of the tank per minute.
2. Calculate the combined filling rate for both pipes:
- When both pipes are open, their combined filling rate is the sum of their individual rates: 1/36 + 1/24 = 3/72 + 4/72 = 7/72 of the tank per minute.
3. Calculate the time it would take for both pipes to fill the tank in 30 minutes:
- Since the combined filling rate is 7/72 of the tank per minute, the time it would take for both pipes to fill the tank in 30 minutes can be calculated as follows:
- Let x be the fraction of the tank filled in 30 minutes.
- We can set up the equation: x = (7/72) * 30.
- Solving for x, we find that the tank would be filled to 7/24 in 30 minutes.
4. Determine how long Pipe Q should be open:
- Since we want the tank to be completely full in 30 minutes, we subtract the fraction of the tank remaining to be filled by Pipe Q from 1.
- 1 - 7/24 = 17/24.
- The time it would take for Pipe Q to fill the remaining 17/24 of the tank can be calculated as follows:
- Let t be the time in minutes.
- We can set up the equation: (1/24) * t = 17/24.
- Solving for t, we find that Pipe Q should be closed after 17 minutes.
Therefore, Pipe Q should be closed after 17 minutes in order to fill the tank in a total of 30 minutes.
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