The sum of ages of A, Band C is 123 years. 5 years ago, the ratio of their ages was 5:9:13 What is A's present age?

Options

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

Answer

To find A's present age given the sum of ages of A, B, and C is 123 years, and the ratio of their ages 5 years ago was 5:9:13, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Present Ages**:
Let A's present age be \( A \), B's present age be \( B \), and C's present age be \( C \).

2. **Set Up the Age Sum Equation**:
According to the problem, the sum of their ages is:
\[ A + B + C = 123 \]

3. **Define Ages 5 Years Ago**:
Five years ago, their ages would be:
- A's age: \( A - 5 \)
- B's age: \( B - 5 \)
- C's age: \( C - 5 \)

4. **Set Up the Ratio Equation**:
The ratio of their ages 5 years ago is given as 5:9:13. Therefore, we can express this as:
\[ \frac{A - 5}{5} = \frac{B - 5}{9} = \frac{C - 5}{13} \]
Let's denote the common ratio as \( k \):
- \( A - 5 = 5k \)
- \( B - 5 = 9k \)
- \( C - 5 = 13k \)

5. **Express A, B, and C in terms of k**:
Rearranging the equations gives:
\[ A = 5k + 5 \]
\[ B = 9k + 5 \]
\[ C = 13k + 5 \]

6. **Substitute into the Sum Equation**:
Substitute \( A \), \( B \), and \( C \) into the sum equation:
\[ (5k + 5) + (9k + 5) + (13k + 5) = 123 \]
Simplifying this gives:
\[ 27k + 15 = 123 \]

7. **Solve for k**:
Subtract 15 from both sides:
\[ 27k = 108 \]
Divide by 27:
\[ k = 4 \]

8. **Find A, B, and C**:
Now substitute \( k \) back to find A, B, and C:
\[ A = 5(4) + 5 = 20 + 5 = 25 \]
\[ B = 9(4) + 5 = 36 + 5 = 41 \]
\[ C = 13(4) + 5 = 52 + 5 = 57 \]

9. **Conclusion**:
A's present age is \( \boxed{25} \).