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?

Options

A. 12 years
B. 11 years
C. 5 years
D. 10 years

Answer

To find the age of the son in the family, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the total age of the father and mother:**
- Given that the average age of the father and mother is 35 years, we can use the formula for average:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of persons}} \]
- Here, the number of persons is 2 (father and mother). Therefore, we can express the total age of the father and mother as:
\[ \text{Total age of father and mother} = \text{Average} \times \text{Number of persons} = 35 \times 2 = 70 \text{ years} \]

2. **Calculate the total age of the father, mother, and son:**
- The average age of the father, mother, and son is given as 27 years. Using the same formula:
\[ \text{Total age of father, mother, and son} = \text{Average} \times \text{Number of persons} = 27 \times 3 = 81 \text{ years} \]

3. **Find the age of the son:**
- Now that we have the total age of the father and mother (70 years) and the total age of the father, mother, and son (81 years), we can find the age of the son by subtracting the total age of the father and mother from the total age of the father, mother, and son:
\[ \text{Age of son} = \text{Total age of father, mother, and son} - \text{Total age of father and mother} = 81 - 70 = 11 \text{ years} \]

### Final Answer:
The age of the son is **11 years**.

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