Ravi has spent a quarter `((1)/(4))` of his life as a boy, one-fifth `((1)/(5))` as a youth, one-third `((1)/(3))` as man and thirteen (13) years in old age. What is his present age?

Options

A. a)70 years
B. b)80 years
C. c)60 years
D. d)65 years

Explanation

To solve the problem of Ravi's present age, we can break it down step by step.

### Step-by-Step Solution:

1. **Define Ravi's Present Age**:
Let Ravi's present age be \( x \).

2. **Express Each Life Stage in Terms of \( x \)**:
- As a boy, he spent \( \frac{1}{4}x \).
- As a youth, he spent \( \frac{1}{5}x \).
- As a man, he spent \( \frac{1}{3}x \).
- In old age, he has spent 13 years.

3. **Set Up the Equation**:
The sum of all the parts of his life should equal his total age:
\[ \frac{1}{4}x + \frac{1}{5}x + \frac{1}{3}x + 13 = x \]

4. **Find a Common Denominator**:
The least common multiple (LCM) of 4, 5, and 3 is 60. We will convert each fraction to have a denominator of 60:
- \( \frac{1}{4}x = \frac{15}{60}x \)
- \( \frac{1}{5}x = \frac{12}{60}x \)
- \( \frac{1}{3}x = \frac{20}{60}x \)

5. **Combine the Fractions**:
Now, we can rewrite the equation:
\[ \frac{15}{60}x + \frac{12}{60}x + \frac{20}{60}x + 13 = x \]
Combining the fractions gives:
\[ \frac{15 + 12 + 20}{60}x + 13 = x \]
Simplifying:
\[ \frac{47}{60}x + 13 = x \]

6. **Isolate \( x \)**:
To isolate \( x \), subtract \( \frac{47}{60}x \) from both sides:
\[ 13 = x - \frac{47}{60}x \]
This simplifies to:
\[ 13 = \frac{60}{60}x - \frac{47}{60}x \]
\[ 13 = \frac{13}{60}x \]

7. **Solve for \( x \)**:
Multiply both sides by \( \frac{60}{13} \):
\[ x = 13 \times \frac{60}{13} \]
\[ x = 60 \]

### Conclusion:
Ravi's present age is **60 years**.