In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?

### Concept & Logic When dealing with average ages of a group, calculate the total sum of the ages. By comparing the total age of the group with a member to the total age of the group without that member, you can easily isolate the individual's age. $$Total\ Age = Average\ Age \times Number\ of\ People$$ ### Step-by-Step Solution * **Given:** The average age of the father and mother is 35 years. * The average age of the father, mother, and son is 27 years. * **Calculation:** Calculate the total age of the parents (2 people). * $Total\ Age\ (Father + Mother) = 35 \times 2 = 70\ years$. * Calculate the total age of the family including the son (3 people). * $Total\ Age\ (Father + Mother + Son) = 27 \times 3 = 81\ years$. * Subtract the total age of the parents from the total age of the whole family to find the son's age. * $Son's\ Age = 81 - 70 = 11\ years$. ### Exam Strategy & Shortcut Use the "Deviation Method." The son joins a group of 2 people whose average is 35, and drags the average down to 27. The drop in average is $35 - 27 = 8$ years. This 8-year drop applies to the 2 original members, meaning a total deficit of $8 \times 2 = 16$ years. The son must be 16 years younger than the new average to cause this drop. So, $27 - 16 = 11$ years. ### Common Pitfall Miscalculating the total number of people in the first group. Some students read "father and a mother" and forget it represents exactly 2 distinct individuals, incorrectly multiplying 35 by 3 or failing to multiply at all. ### Final Answer **Therefore, the correct answer is 11 years.**