2 pipes A and B can fill a tank in 20 minutes and 30 minutes respectively.…

Answer: 7.5 min

Explanation:

Let the first pipe's rate (A) be 1/20 tank per minute and the second pipe's rate (B) be 1/30 tank per minute.

If both pipes run together for x minutes and then only the first pipe runs for the remaining (15 − x) minutes, the total work done equals one full tank:

(1/20 + 1/30)·x + (1/20)·(15 − x) = 1

Compute the combined rate: 1/20 + 1/30 = 1/12. So the equation becomes:

(1/12)x + (1/20)(15 − x) = 1

Multiply both sides by 60 to clear denominators: 5x + 3(15 − x) = 60

Simplify: 5x + 45 − 3x = 60 ⇒ 2x = 15 ⇒ x = 7.5

Therefore, the second pipe should be turned off after 7.5 minutes so the tank is filled exactly at 15 minutes.