Multiple choice

Two pipes A and B can fill a cistern in $30$ min and $40$ min respectively, Both the pipes are turned on simultaneously. When should the second pipe be closed if the cistern is to be filled in $24$ min ?

  1. $6$ min
  2. $8$ min
  3. $10$ min
  4. $12$ min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/30 per min, Pipe B fills 1/40 per min. Let B be open for x minutes. Then (1/30 + 1/40) * x + (1/30) * (24-x) = 1. Solving (7/120) * x + (24-x)/30 = 1, multiplying by 120 gives 7x + 4(24-x) = 120, so 3x + 96 = 120, 3x = 24, x = 8.

AI explanation

Pipe A runs for the full 24 minutes at a rate of 1/30 per minute, filling 24/30 or 4/5 of the cistern. The remaining 1/5 must be filled by pipe B, whose rate is 1/40 per minute. Dividing the remaining work by B's rate gives (1/5) / (1/40) = 8 minutes, so B should be closed after 8 minutes. The result is 8 min.

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