Multiple choice

A pipe can fill a tank in 20 minutes and another pipe can fill it in 30 minutes. A person opens both the pipes simultaneously. When the tank should have been full, he finds that the drain pipe is open. He then closes the drain pipe and after three minutes, the tank is full. In how much time can the drain pipe empty the tank?

  1. 50 min

  2. 48 min

  3. 44 min

  4. 38 min

  5. 60 min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/20 per min, Pipe B 1/30 per min. Combined = 1/12 per min. In 12 mins, they fill 1 tank. If drain pipe D is open, net rate = 1/12 - 1/D. After 12 mins, they filled (1/12 - 1/D)*12. Then D closes, and A+B fill the rest in 3 mins: (1/12)*3 = 1/4. Total = 1. Solving gives D = 48.

AI explanation

Using the LCM method, assume the tank capacity is 60 units. The rates of the two filling pipes are 3 and 2 units per minute, so their combined rate is 5 units per minute. After the drain pipe is closed, the remaining part is filled in 3 minutes at this rate, meaning the remaining part was 15 units. Therefore, the drain pipe had emptied 45 units in the time it took the two pipes to almost fill the tank, which is 9 minutes. The drain pipe's rate is 45 divided by 9, or 5 units per minute, so it takes 48 minutes to empty the full tank.

Keep practicing — related questions