Multiple choice general knowledge math & puzzles

Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?

  1. (2/3)a hours

  2. (3/2)a hours

  3. 3/4)a hours

  4. (5/3) a hours

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills in a hours, so rate = 1/a tank per hour. With the leak, effective rate = 1/(3a). Let leak rate = -1/x (negative because it empties). Then 1/a - 1/x = 1/(3a). Solving: 1/x = 1/a - 1/(3a) = 2/(3a), so x = (3/2)a hours.