The sum of ages of 6 Persons A, B, C, D, E and F in a company born at the intervals of 5 years each is 105 years. What is the age of the oldest person? Options are (a) 25 years (b) 15 years (c) 30 years (d) 20 years.

Options

A. 25 years
B. 15 years
C. 30 years
D. 20 years

Answer

To solve the problem of finding the age of the oldest person among six individuals whose ages are in an arithmetic progression (AP) and sum up to 105 years, we can follow these steps:

### Step-by-step Solution:

1. **Understanding the Problem**:
- We have 6 persons (A, B, C, D, E, F) whose ages are in an arithmetic progression with a common difference of 5 years.
- The sum of their ages is given as 105 years.

2. **Setting Up the Arithmetic Progression**:
- Let the age of the first person (A) be \( A \).
- The ages of the other persons can be expressed as:
- B = A + 5
- C = A + 10
- D = A + 15
- E = A + 20
- F = A + 25

3. **Calculating the Sum of Ages**:
- The sum of their ages can be written as:
\[ A + (A + 5) + (A + 10) + (A + 15) + (A + 20) + (A + 25) = 105 \]
- Simplifying this, we have:
\[ 6A + (5 + 10 + 15 + 20 + 25) = 105 \]
- The sum of the numbers in parentheses is:
\[ 5 + 10 + 15 + 20 + 25 = 75 \]
- Therefore, the equation becomes:
\[ 6A + 75 = 105 \]

4. **Solving for A**:
- Rearranging the equation gives:
\[ 6A = 105 - 75 \]
\[ 6A = 30 \]
\[ A = 5 \]

5. **Finding the Age of the Oldest Person**:
- The oldest person is F, whose age can be calculated as:
\[ F = A + 25 = 5 + 25 = 30 \]

6. **Conclusion**:
- Therefore, the age of the oldest person is **30 years**.

### Final Answer:
- The age of the oldest person is **30 years** (Option C).