The average age of four brothers is 12 years. If the age of their mother is also included, the average is increased by 5 years. The age of the mother (in years) is :

Options

A. 37 years
B. 43 years
C. 48 years
D. 53 years

Answer

To solve the problem step by step, let's break it down:

1. **Understanding the Average Age of the Four Brothers**:
- The average age of the four brothers is given as 12 years.
- To find the total age of the four brothers, we multiply the average age by the number of brothers:
\[ \text{Total age of four brothers} = \text{Average age} \times \text{Number of brothers} = 12 \times 4 = 48 \text{ years} \]

2. **Including the Mother's Age**:
- When the age of the mother is included, the average age increases by 5 years. Therefore, the new average age becomes:
\[ \text{New average age} = 12 + 5 = 17 \text{ years} \]

3. **Calculating the Total Age Including the Mother**:
- Now, we need to find the total age of the four brothers and their mother. Since the average age of five individuals (four brothers and one mother) is 17 years, we can calculate the total age:
\[ \text{Total age of four brothers and mother} = \text{New average age} \times \text{Total number of individuals} = 17 \times 5 = 85 \text{ years} \]

4. **Finding the Mother's Age**:
- To find the age of the mother, we subtract the total age of the four brothers from the total age of the four brothers and their mother:
\[ \text{Mother's age} = \text{Total age of four brothers and mother} - \text{Total age of four brothers} = 85 - 48 = 37 \text{ years} \]

Thus, the age of the mother is **37 years**.