Multiple choice

The average age of a class of 25 boys is 15 years 4 months. The average of the first 9 boys is 16 years 4 months and that of the next 13 boys is 14 years one month. Find the average age of the remaining three.

  1. 16 years

  2. 17 years 9 months

  3. 18 years 11 months

  4. 12 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age = 25 * (15 + 4/12) = 25 * 15.333 = 383.33 years. First 9: 9 * (16 + 4/12) = 9 * 16.333 = 147 years. Next 13: 13 * (14 + 1/12) = 13 * 14.0833 = 183.0833 years. Remaining 3: 383.33 - 147 - 183.0833 = 53.25 years. Average = 53.25 / 3 = 17.75 years, which is 17 years 9 months.

AI explanation

Convert all ages to months: the total age for 25 boys is 25 times 184 months, equaling 4600 months. The total age for the first 9 boys is 9 times 196 months (1764 months) and for the next 13 boys is 13 times 169 months (2197 months). The total age of these 22 boys is 3961 months, so the total age of the remaining 3 boys is 4600 minus 3961, which equals 639 months. Dividing 639 months by 3 gives 213 months per boy, which equals 17 years and 9 months.

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