Two pipes P and Q can fill a tank in 36 minutes and 45 minutes, respectively. If both pipes are opened together, what is the time taken to fill the tank?

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Accepted Answer

Let the total capacity of the tank be 1 unit.

Pipe P fills the tank in 36 minutes, so its rate = 1/36 tank per minute.
Pipe Q fills the tank in 45 minutes, so its rate = 1/45 tank per minute.

Combined rate = 1/36 + 1/45
To add, take LCM of 36 and 45, which is 180.
1/36 = 5/180
1/45 = 4/180
So, combined rate = (5 + 4)/180 = 9/180 = 1/20 tank per minute.

Time taken to fill the tank = 1 / (1/20) = 20 minutes.

So, the correct answer is 20 minutes.

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