Multiple choice

The number of children in a camp is x and their average weight is 20 kg. If 5 children, each weighing 12 kg, join the camp or if 10 children, each weighing 21 kg, leave the camp, then the average weight in both the cases remains the same. The value of x is

  1. 18

  2. 16

  3. 15

  4. 14
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C Correct answer
Explanation

Let x be the number of children. The total weight is 20x. Setting up the equations for the two scenarios: (20x + 5*12)/(x+5) = 20 and (20x - 10*21)/(x-10) = 20. Solving either yields x = 15.

AI explanation

For the first case, the total weight becomes 20 times x plus 60, and the new average is (20x plus 60) divided by (x plus 5). For the second case, the total weight becomes 20 times x minus 210, and the new average is (20x minus 210) divided by (x minus 10). Equating the two averages gives (20x plus 60) divided by (x plus 5) equals (20x minus 210) divided by (x minus 10). Cross-multiplying and solving yields 400x equals 6000. The result is x equals 15.

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