If the average age of four children is 12 years and the average age of these children and their father is 20 years, what is the age of the father ?

Options

A. 52 years
B. 48 years
C. 62 years
D. 54 years

Answer

To find the age of the father based on the given information, we can follow these steps:

### Step 1: Calculate the total age of the four children.
The average age of the four children is given as 12 years. The formula for average is:

\[ \text{Average} = \frac{\text{Total Age}}{\text{Number of Children}} \]

So, we can rearrange the formula to find the total age:

\[ \text{Total Age of Children} = \text{Average Age} \times \text{Number of Children} \]

Substituting the values:

\[ \text{Total Age of Children} = 12 \times 4 = 48 \text{ years} \]

### Step 2: Calculate the total age of the four children and their father.
The average age of the four children and their father is given as 20 years. Using the same average formula:

\[ \text{Total Age of Children and Father} = \text{Average Age} \times \text{Number of People} \]

Here, the number of people is 5 (4 children + 1 father):

\[ \text{Total Age of Children and Father} = 20 \times 5 = 100 \text{ years} \]

### Step 3: Calculate the age of the father.
Now, we can find the age of the father by subtracting the total age of the children from the total age of the children and their father:

\[ \text{Age of Father} = \text{Total Age of Children and Father} - \text{Total Age of Children} \]

Substituting the values we have:

\[ \text{Age of Father} = 100 - 48 = 52 \text{ years} \]

### Final Answer:
The age of the father is **52 years**.

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