There were 24 students in a class. One of them, who was 18 years old, left the class and his place was filled up by a newcomer. If the average of the class thereby, was lowered by one month, the age of the newcomer is

### Concept & Strategy When a member is replaced and the overall average decreases, the incoming member must have a lower value than the departing member. The new person's value equals the old person's value *minus* the total decrease distributed across the whole group. $$New\ Value = Replaced\ Value - (Number\ of\ Entities \times Decrease\ in\ Average)$$ ### Step-by-Step Solution * **Standardize units:** The student who left is 18 years old, but the average decrease is given in months. Decrease in average = 1 month. * **Calculate the total age decrease:** The average drops by 1 month for all 24 students. $$Total\ Decrease = 24 \times 1\text{ month} = 24\text{ months}$$ * **Convert total decrease back to years:** $$24\text{ months} = 2\text{ years}$$ * **Determine the newcomer's age:** The newcomer must be 2 years younger than the person who left in order to cause this drop. $$Newcomer = 18\text{ years} - 2\text{ years}$$ $$Newcomer = 16\text{ years}$$ ### Exam Strategy & Shortcut Directly apply the deviation formula while paying close attention to units. Mentally calculate: $24 \times 1 \text{ month} = 24 \text{ months}$, which is exactly $2 \text{ years}$. Since the average *lowered*, subtract this from the departed student's age: $18 - 2 = 16$. ### Common Pitfall Failing to convert units. Many students subtract 1 directly from 18, mistakenly getting 17, completely ignoring that the decrease is 1 *month*, not 1 *year*. Always align your units before adding or subtracting. ### Final Answer **Therefore, the correct answer is 16 years.**