Multiple choice

A cistern has three pipes A, B and C. A and B can fill it in 3 hours and 4 hours respectively while C can empty a completely filled tank in 1 hour. If three pipes are opened at 3, 4 and 5 pm, then at what time will the cistern be empty?

  1. 6:15pm

  2. 7:12pm

  3. 8:12pm

  4. 8:35pm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/3 per hour, B fills 1/4 per hour, C empties 1/1 per hour. Net rate = 1/3 + 1/4 - 1 = -5/12. By 5pm, A has worked 2 hours (2/3 filled) and B has worked 1 hour (1/4 filled). Total filled = 2/3 + 1/4 = 11/12. The tank empties at a rate of 5/12 per hour. Time to empty = (11/12) / (5/12) = 2.2 hours = 2 hours 12 minutes after 5pm, which is 7:12pm.

AI explanation

Let the total work be 12 units, where A fills 4 units per hour, B fills 3 units per hour, and C empties 12 units per hour. Between 3 pm and 4 pm, A fills 4 units, and between 4 pm and 5 pm, A and B together add 7 units, bringing the total to 11 units by 5 pm. From 5 pm onwards, the net rate is 4 plus 3 minus 12, giving a loss of 5 units per hour, so after 1 hour the tank has 6 units, and after another hour it has 1 unit. The final unit is emptied at a net rate of 9 units per hour, since A and B close while C continues emptying, taking 1/9 of an hour, which equals 6 minutes and 40 seconds; the tank is completely empty at exactly 7:12 pm.

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