Multiple choice

Pipes X and Y can fill a tank in 8 hr and 12 hr, respectively. It happened that Shamu opened pipe X at 8 am and forgot to open pipe Y. After 120 min, he realised the mistake and then opened the other pipe. At what time will the tank be full?

  1. 11.36 pm

  2. 12.36 pm

  3. 1.36 pm

  4. 2.36 pm

  5. 3.36 pm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe X fills 1/8 per hour, Y fills 1/12 per hour. In 2 hours, X fills 2/8 = 1/4. Remaining 3/4. Combined rate = 1/8 + 1/12 = 5/24. Time = (3/4) / (5/24) = 18/5 = 3.6 hours (3 hours 36 minutes). Start time 10 am (after 2 hours), so 10 am + 3h 36m = 1:36 pm.

AI explanation

Pipe X runs alone for 120 minutes, or 2 hours, filling 2/8 or 1/4 of the tank and leaving 3/4 unfilled. When both pipes are open, their combined hourly rate is 1/8 + 1/12 = 3/24 + 2/24 = 5/24. The time needed to fill the remaining 3/4 of the tank at this combined rate is (3/4) / (5/24) = 18/5 hours, or 3 hours and 36 minutes. Adding this duration to the start time of 8 am plus the initial 2 hours means the tank will be full at 1:36 pm.

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