Multiple choice

Two pipes P and Q can fill a cistern in 18 min. and 24 min. respectively. They start filling together and after 6 min. Pipe Q gets closed. In how much time the whole tank will be filled ?

  1. 15min

  2. 15.5min

  3. 13.5min

  4. 13min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined rate = 1/18 + 1/24 = 4/72 + 3/72 = 7/72. In 6 minutes, they fill 6 * 7/72 = 42/72 = 7/12. Remaining = 5/12. Pipe P fills at 1/18. Time for P to fill 5/12 = (5/12) * 18 = 7.5 minutes. Total time = 6 + 7.5 = 13.5 minutes.

AI explanation

Pipes P and Q have filling rates of 1/18 and 1/24 of the tank per minute respectively, so their combined rate is 1/18 + 1/24 = 7/72. Working together for 6 minutes, they fill 6 times 7/72, which equals 42/72 or 7/12 of the tank, leaving 5/12 empty. Pipe P alone fills at 1/18 per minute, so to fill the remaining 5/12 it takes (5/12) divided by (1/18), equalling 7.5 minutes. The total time to fill the tank is 6 + 7.5, which is 13.5 minutes.

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