Multiple choice

Two taps M and N can separately fill a cistern in $30$ and $20$ minutes respectively. They started to fill a cistern together but tap M is turned off after few minutes and tap N fills the rest part of cistern in $5$ minutes. After how many minutes was tap M turned-off?

  1. $9$ min
  2. $10$ min
  3. $11$ min
  4. $12$ min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M and N work for x minutes. N works for an additional 5 minutes. (x/30) + (x+5)/20 = 1. Multiply by 60: 2x + 3(x+5) = 60. 2x + 3x + 15 = 60. 5x = 45. x = 9 minutes.

AI explanation

Using the rates of work method, tap N fills the remaining part in 5 minutes, completing 5/20 or 1/4 of the cistern; this means 3/4 of the cistern was filled by both taps working together. The combined filling rate of taps M and N is 1/30 plus 1/20, which equals 1/12 of the cistern per minute. The time they worked together is the portion of the cistern they filled divided by their combined rate, so 3/4 divided by 1/12 equals 9 minutes. Therefore, tap M was turned off after 9 minutes.

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