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Two pipes P and Q can fill a tank in 24 minutes and 16 minutes respectively. If both the pipes are opened simultaneously, after how much time Q should be closed so that the tank will be filled completely in 12 minutes?
  • a)
    8 minutes
  • b)
    6 minutes
  • c)
    5 minutes
  • d)
    4 minutes
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two pipes P and Q can fill a tank in 24 minutes and 16 minutes respec...
To solve this problem, we can use the concept of work. The work done by a pipe is defined as the product of its rate of work (or filling rate) and the time it is open.

Let's assume that the capacity of the tank is 1 unit.

Pipe P fills the tank in 24 minutes, so its rate of work is 1/24 units per minute.
Pipe Q fills the tank in 16 minutes, so its rate of work is 1/16 units per minute.

Let's say Q is open for t minutes before it is closed.

The work done by P in 12 minutes is (1/24) * 12 = 1/2 units.
The work done by Q in t minutes is (1/16) * t = t/16 units.

Since the tank is completely filled in 12 minutes, the total work done by both pipes should be equal to 1 unit. Therefore, we can write the equation:

1/2 + t/16 = 1

Simplifying the equation, we get:
8 + t = 16
t = 8

Therefore, Q should be closed after 8 minutes.

Thus, the correct answer is option A) 8 minutes.
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Community Answer
Two pipes P and Q can fill a tank in 24 minutes and 16 minutes respec...
Let the pipe Q be closed after x minutes
Part filled by P in 12 minutes + part filled by Q in x minutes = 1
12 /24 + x /16 = 1
x = 8 minutes
Hence, pipe Q must be closed after 8 minutes.
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