Multiple choice

The average weight of $9$ men is x kg. After another men joins the group, the average increases by $6\%$. Still another man joins and average returns to old level of x kg. Which one of the following true?

  1. The $10^{th}$ & $11^{th}$ men weight same
  2. The $10^{th}$ man weight half as much as the $11^{th}$ man
  3. The $10^{th}$ man weight as much as the $11^{th}$ man

  4. None of these
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D Correct answer
AI explanation

Let the initial average weight of the 9 men be x, making their total weight 9x. When the 10th man joins, the average increases by 6 percent, making the new average 1.06x, so the new total weight is 10 multiplied by 1.06x, which is 10.6x. This means the 10th man weighs 10.6x minus 9x, which is 1.6x. When the 11th man joins, the average returns to x, meaning the new total weight for 11 men is 11x. The 11th man's weight is 11x minus 10.6x, which is 0.4x. The weight of the 10th man is 1.6x and the weight of the 11th man is 0.4x, meaning the 10th man weighs four times as much as the 11th man, which does not match any provided scenario.

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