Multiple choice

Two taps can separately fill a cistern in $10$ minutes and $15$ minutes, respectively and when the waste pipe is open, they can together fill it in $18$ minutes. The waste pipe can empty the full cistern in:

  1. $7$ min
  2. $9$ min
  3. $13$ min
  4. $23$ min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the capacity be 90 units. Tap A fills 9 units/min and Tap B fills 6 units/min. Together they fill 15 units/min. With the waste pipe, they fill 90/18 = 5 units/min. The waste pipe must remove 15 - 5 = 10 units/min, so it empties the cistern in 90/10 = 9 minutes.

AI explanation

Using the LCM method, let the total capacity be 90 units. The two filling taps work at rates of 9 units and 6 units per minute respectively, giving a combined filling rate of 15 units per minute. The net rate when the waste pipe is open is 90 units divided by 18 minutes, which is 5 units per minute, meaning the waste pipe empties at a rate of 10 units per minute. Dividing the total capacity of 90 units by the waste pipe rate of 10 units per minute results in 9 minutes.

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