Explanation:

- A and B's profits depend on their capital and the time their capital was invested.

- A invested for 24 months, B invested for 8 months. Let's denote A's capital as Rs. X.

- Given, the profit ratio between A and B is 21:16.

- Relationship: \( \frac{A's \: Capital \: \times \: A's \: Time}{B's \: Capital \: \times \: B's \: Time} = \frac{A's \: Profit}{B's \: Profit} \)

- Plugging values: \( \frac{X \times 24}{32000 \times 8} = \frac{21}{16} \)

- Simplifying: \( \frac{24X}{256000} = \frac{21}{16} \)

- Further simplification gives: \( 24X \times 16 = 21 \times 256000 \)

- Solving: \( 384X = 5376000 \)

- Therefore, \( X = \frac{5376000}{384} \)

- Calculation gives X = Rs. 14,000.

Correct Answer: Option 2, Rs. 14,000