Explanation:

- We start with a bike purchased for Rs50,000.

- The value depreciates at 10% annually.

- We need to find the number of years until the value reaches Rs36,450.

- The formula for depreciation is:

\( \text{Final Value} = \text{Initial Value} \times (1 - \text{Depreciation Rate})^{\text{Years}} \).

- Plugging in the values:

\( 36,450 = 50,000 \times (0.9)^{\text{Years}} \).

- Calculate based on options:

- Option 1: 3 years

- \( 50,000 \times 0.9^3 = 50,000 \times 0.729 = 36,450 \).

Correct, matches target value.

- Option 2: 2 years

- \( 50,000 \times 0.9^2 = 40,500 \).

- Too high.

- Option 3: 5 years

- \( 50,000 \times 0.9^5 \approx 29,500 \).

- Too low.

- Option 4: 4 years

- \( 50,000 \times 0.9^4 \approx 32,805 \).

- Still too low.

- Correct Answer: Option 1: 3 years.

- .