The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother

Options

A. 40
B. 41
C. 42
D. 43

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total age of the mother and her six children.
Given that the average age of the mother and her six children is 12 years, we can calculate the total age of the group.

- Total number of people = 1 (mother) + 6 (children) = 7
- Average age = 12 years

Using the formula for average:
\[ \text{Total Age} = \text{Average Age} \times \text{Number of People} \]
\[ \text{Total Age} = 12 \times 7 = 84 \text{ years} \]

### Step 2: Calculate the average age without the mother.
When the mother is excluded, the average age of the six children is reduced by 5 years.

- New average age without the mother = 12 - 5 = 7 years

### Step 3: Calculate the total age of the six children.
Using the new average age:
\[ \text{Total Age of Children} = \text{New Average Age} \times \text{Number of Children} \]
\[ \text{Total Age of Children} = 7 \times 6 = 42 \text{ years} \]

### Step 4: Calculate the age of the mother.
Now, we can find the age of the mother by subtracting the total age of the children from the total age of the group (mother + children).

\[ \text{Age of Mother} = \text{Total Age with Mother} - \text{Total Age of Children} \]
\[ \text{Age of Mother} = 84 - 42 = 42 \text{ years} \]

### Conclusion:
The age of the mother is **42 years**.

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