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Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes?
- a)14 minutes
- b)12 minutes
- c)15 minutes
- d)18 minutes
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
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Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respect...
Required time = y(1-(t/x)) = 27(1-(8/24))= 18 minutes
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Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respect...
Problem Statement:
Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes?
Solution:
Let the time for which Pipe Q should be open be x minutes.
Pipe P fills the tank in 24 minutes, so in 1 minute it can fill 1/24th of the tank.
Pipe Q fills the tank in 27 minutes, so in 1 minute it can fill 1/27th of the tank.
If both pipes are opened, then in 1 minute they can fill (1/24 + 1/27) of the tank.
So, in 8 minutes they can fill (8/24 + 8/27) of the tank.
We need to find the time for which Pipe Q should be open, so that the tank is full in 8 minutes.
Let the volume of the tank be V.
According to the problem statement, we have:
(V/(8-x)) = (8/24 + 8/27)
Simplifying this equation, we get:
V = (8/24 + 8/27) * (8-x)
V = (2/3 + 8/27) * (8-x)
V = (70/81) * (8-x)
V = 560/81 - (70/81)x
Now, since Pipe Q should be closed before the tank is full, we have:
V = (1/24)*8 + (1/27)*x
V = 1/3 + (1/27)*x
Substituting the value of V from the previous equation, we get:
560/81 - (70/81)x = 1/3 + (1/27)*x
Solving for x, we get:
x = 18 minutes
Therefore, Pipe Q should be closed after 18 minutes of opening both the pipes so that the tank is full in 8 minutes.
Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes?
Solution:
Let the time for which Pipe Q should be open be x minutes.
Pipe P fills the tank in 24 minutes, so in 1 minute it can fill 1/24th of the tank.
Pipe Q fills the tank in 27 minutes, so in 1 minute it can fill 1/27th of the tank.
If both pipes are opened, then in 1 minute they can fill (1/24 + 1/27) of the tank.
So, in 8 minutes they can fill (8/24 + 8/27) of the tank.
We need to find the time for which Pipe Q should be open, so that the tank is full in 8 minutes.
Let the volume of the tank be V.
According to the problem statement, we have:
(V/(8-x)) = (8/24 + 8/27)
Simplifying this equation, we get:
V = (8/24 + 8/27) * (8-x)
V = (2/3 + 8/27) * (8-x)
V = (70/81) * (8-x)
V = 560/81 - (70/81)x
Now, since Pipe Q should be closed before the tank is full, we have:
V = (1/24)*8 + (1/27)*x
V = 1/3 + (1/27)*x
Substituting the value of V from the previous equation, we get:
560/81 - (70/81)x = 1/3 + (1/27)*x
Solving for x, we get:
x = 18 minutes
Therefore, Pipe Q should be closed after 18 minutes of opening both the pipes so that the tank is full in 8 minutes.
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Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes?a)14 minutesb)12 minutesc)15 minutesd)18 minutese)None of the AboveCorrect answer is option 'D'. Can you explain this answer?
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