Multiple choice

A cistern can be filled up by one pipe in 12 hours and by another in 8 hours. Both the pipes are kept open for $2\displaystyle\frac{1}{2}$ hours. The part of the cistern filled up is

  1. $\displaystyle\frac{25}{48}$
  2. $\displaystyle\frac{5}{6}$
  3. $\displaystyle\frac{25}{36}$
  4. $\displaystyle\frac{12}{25}$
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A Correct answer
Explanation

Pipe 1 rate = 1/12 per hour. Pipe 2 rate = 1/8 per hour. Combined rate = 1/12 + 1/8 = 2/24 + 3/24 = 5/24 per hour. In 2.5 (5/2) hours, the filled part is (5/24) * (5/2) = 25/48.

AI explanation

The first pipe fills at a rate of 1/12 of the cistern per hour and the second pipe fills at 1/8 per hour, so their combined rate is 1/12 + 1/8 = 5/24 per hour. Over 2 1/2 hours, the fraction of the cistern filled is 5/24 * 5/2 = 25/48.

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