The average age of a man and his two twin sons born on the same day is 30 yr. The ratio of the ages of father and one son is 5 : 2, what is the father's age?

Options

A. 50 yr
B. 30 yr
C. 45 yr
D. 20 yr

Answer

To solve the problem step by step, we will follow the information given in the question and apply the necessary mathematical concepts.

### Step-by-Step Solution:

1. **Understanding the Average**:
The average age of the man and his two twin sons is given as 30 years. The average is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of people}} \]
Here, the number of people is 3 (the father and his two sons).

2. **Calculating the Sum of Ages**:
Using the average, we can find the sum of their ages:
\[ \text{Sum of ages} = \text{Average} \times \text{Number of people} = 30 \times 3 = 90 \text{ years} \]

3. **Setting Up the Ratio**:
The ratio of the ages of the father to one son is given as 5:2. Let’s denote the age of the father as \(5x\) and the age of one son as \(2x\). Since there are two sons, the age of the second son will also be \(2x\).

4. **Expressing the Total Age in Terms of x**:
The total age can be expressed as:
\[ \text{Total age} = \text{Father's age} + \text{Age of first son} + \text{Age of second son} = 5x + 2x + 2x = 9x \]

5. **Setting Up the Equation**:
We know from step 2 that the total age is 90 years, so we can set up the equation:
\[ 9x = 90 \]

6. **Solving for x**:
To find \(x\), divide both sides of the equation by 9:
\[ x = \frac{90}{9} = 10 \]

7. **Finding the Father's Age**:
Now, we can find the father's age using the value of \(x\):
\[ \text{Father's age} = 5x = 5 \times 10 = 50 \text{ years} \]

### Conclusion:
The father's age is **50 years**.