Pipe A can fill a tank in 20 min and B can fill the tank in 30 min. Pipe A is opened for half the time and pipe B and A are opened for other half of the time. How long it will take to fill the tank?

15 min

Lets assume the time to fill the tank is T hours.

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Now, according to question:

⇒ A works for 1st half of the time and

⇒ A and B work for second half of the time.

Here, we can conclude that;

⇒ A works for full time and

⇒ B works for only half of the time.

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Note: Here, we can say the time taken by B for working half of the time is equals to the time taken by B for working full time with his half efficiency.

So,  A's efficiency = 3 ltr/min

B's efficiency =1 ltr/min

ATQ,

Tank will be fill in = \(\frac{60}{3\;+\;1}\) = 15min