The average age of a group of four men whose ages are in the ratio of 2 :3: 4 :5 is 42 yr, what is the age of the eldest person in this group?

Options

A. 60
B. 48
C. 36
D. 214

Answer

To solve the problem, we need to find the age of the eldest person in a group of four men whose ages are in the ratio 2:3:4:5, given that their average age is 42 years.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ages of the four men are in the ratio 2:3:4:5. We can express their ages in terms of a variable \( x \):
- First man's age = \( 2x \)
- Second man's age = \( 3x \)
- Third man's age = \( 4x \)
- Fourth man's age = \( 5x \)

2. **Calculate the Total Age**:
The total age of the four men can be calculated by adding their ages:
\[ \text{Total Age} = 2x + 3x + 4x + 5x = 14x \]

3. **Use the Average Age**:
We know the average age of the four men is 42 years. The formula for average age is:
\[ \text{Average Age} = \frac{\text{Total Age}}{\text{Number of Persons}} \]
Substituting the values we have:
\[ 42 = \frac{14x}{4} \]

4. **Solve for \( x \)**:
To find \( x \), we can multiply both sides of the equation by 4:
\[ 42 \times 4 = 14x \]
This simplifies to:
\[ 168 = 14x \]
Now, divide both sides by 14:
\[ x = \frac{168}{14} = 12 \]

5. **Calculate Each Man's Age**:
Now that we have \( x \), we can find the ages of each man:
- First man's age = \( 2x = 2 \times 12 = 24 \) years
- Second man's age = \( 3x = 3 \times 12 = 36 \) years
- Third man's age = \( 4x = 4 \times 12 = 48 \) years
- Fourth man's age = \( 5x = 5 \times 12 = 60 \) years

6. **Identify the Eldest Person**:
The eldest person is the one with the highest age. From our calculations, the ages are:
- 24 years
- 36 years
- 48 years
- 60 years

Therefore, the eldest person is 60 years old.

### Final Answer:
The age of the eldest person in this group is **60 years**.