Explanation:

Sure! Let's break it down step by step:

- First, note the formula for simple interest: \( \text{Simple Interest} = \frac{P \times R \times T}{100} \), where \( P \) is the principal, \( R \) is the rate, and \( T \) is the time in years.

- Here, the principal \( P \) is Rs 30,000, the final amount after interest is Rs 38,400, making the interest earned \( 38,400 - 30,000 = Rs 8,400 \).

- The rate \( R \) is given as 8% per annum.

- Plugging these into the formula:

$$

8,400 = \frac{30,000 \times 8 \times T}{100}

$$

- Simplifying:

$$

8,400 = 2,400 \times T

$$

- Solving for \( T \):

$$

T = \frac{8,400}{2,400} = 3.5

$$

- This means the investment was made for 3.5 years.

- So, the correct option is Option 1: 3.5.