Multiple choice

The average age of children in a room is 32 years. 9 more children join the children in the same room whose average age is 26 years, and thereby decrease the average age of the all the children in the room by 3 years. Find the number of children in the room initially.

  1. 5

  2. 9

  3. 11

  4. 17

  5. 22
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the initial number of children. Total age = 32n. New total age = 32n + 9 * 26. New average = (32n + 234) / (n + 9) = 32 - 3 = 29. 32n + 234 = 29n + 261 => 3n = 27 => n = 9.

AI explanation

Let the initial number of children be N. The sum of the ages of the initial children is 32N, and the sum of the ages of the 9 new children is 9 multiplied by 26, which is 234. The new average age of all the children is 32 minus 3, equaling 29 years, so the total age of all children becomes 29 multiplied by (N plus 9). Equating the total ages gives 32N plus 234 equals 29N plus 261, meaning 3N equals 27, so the initial number of children is 9.

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