3 years ago, the ratio of Ramesh's and Suresh's age was 5 : 9. After 5 years this ratio would be 3 : 5. The present age of Suresh is :

Question

Accepted Answer

To determine the present age of Suresh, we need to analyze the information given in the problem and verify why Option 1 (75 Years) is the correct answer.

### Explanation:

1. **Understanding the Problem:**
   - **3 years ago:** The ratio of Ramesh's age to Suresh's age was 5:9.
   - **5 years from now:** The ratio of their ages will be 3:5.

2. **Setting Up Equations:**
   - Let the ages of Ramesh and Suresh 3 years ago be $5x$ and $9x$ respectively.
   - Therefore, the present ages of Ramesh and Suresh are $5x + 3$ and $9x + 3$.

3. **Future Age Condition:**
   - In 5 years, their ages will be $5x + 8$ and $9x + 8$.
   - According to the problem, the ratio of their ages will be 3:5.
   - Therefore, we can set up the equation:
     $$
     \frac{5x + 8}{9x + 8} = \frac{3}{5}
     $$

4. **Solving the Equation:**
   - Cross-multiply to solve for $x$:
     $$
     5(5x + 8) = 3(9x + 8)
     $$
     $$
     25x + 40 = 27x + 24
     $$
     $$
     27x - 25x = 40 - 24
     $$
     $$
     2x = 16
     $$
     $$
     x = 8
     $$

5. **Calculating Present Ages:**
   - The present age of Suresh is $9x + 3 = 9(8) + 3 = 72 + 3 = 75$.

### Justification for Option 1:

- **Option 1 (75 Years):** This is the correct answer as calculated above. The present age of Suresh, based on the given conditions and solving the equations, is indeed 75 years.

### Explanation for Incorrect Options:

- **Option 2 (43 Years):** This option is incorrect because substituting 43 into the equations does not satisfy the given age ratios.
- **Option 3 (72 Years):** This option is incorrect because it does not align with the calculated value of 75 years for Suresh's present age.
- **Option 4 (40 Years):** This option is incorrect as it does not meet the conditions set by the problem regarding the age ratios.

In conclusion, the detailed calculations and logical reasoning confirm that Option 1 (75 Years) is the correct answer for Suresh's present age.