Explanation:

To solve the problem, let's look at both investments:

- A's Investment:

- Compound Interest formula: \(A = P(1 + \frac{r}{100})^n\)

- Principal (P) = Rs. x, Rate (r) = 20%, Time (n) = 2 years.

- Compound amount = \(x(1.2)^2 = x \times 1.44\)

- Compound interest earned = Amount - Principal = \(1.44x - x = 0.44x\)

- B's Investment:

- Simple Interest (SI) formula: \(SI = \frac{P \times r \times n}{100}\)

- Principal (P) = Rs. 2x, Rate (r) = 10%, Time (n) = 3 years.

- Simple interest earned = \(\frac{2x \times 10 \times 3}{100} = 0.6x\)

- The difference in interest earned between A and B is Rs. 2400.

- $$0.6x - 0.44x = 2400$$

- $$0.16x = 2400$$

- $$x = \frac{2400}{0.16} = 15000$$

- Therefore, the value of 'x' is Rs. 15,000.

Correct Answer: Option 1