Multiple choice

Pipe A can fill a tank in 12 hours and pipe B can empty the tank in 18 hours. Both pipes are opened at 6 AM and after some time, pipe B is closed and tank is full at 8 PM. At what time was the pipe B closed?

  1. 10 AM

  2. 8 AM

  3. 9 AM

  4. 11 AM
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let pipe B be closed after x hours. Pipe A runs for 14 hours (6 AM to 8 PM). Pipe A fills 14/12 of the tank. Pipe B empties x/18 of the tank. Since the tank is full, 14/12 - x/18 = 1. 7/6 - x/18 = 1. x/18 = 1/6. x = 3 hours. 6 AM + 3 hours = 9 AM.

AI explanation

Using the least common multiple method, let the total capacity of the tank be 36 units. Pipe A fills 3 units per hour and pipe B empties 2 units per hour. The tank is full at 8 PM, meaning from 6 AM to 8 PM is 14 hours, during which pipe A works alone to fill the remaining tank after B is closed. If B was closed after y hours, the net fill while both were open was y units, and the remaining (36 minus y) units were filled by A in 14 hours. Setting 36 minus y equal to 3 multiplied by 14 gives y = 6, meaning pipe B was closed at 9 AM.

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