Explanation:

- A invested Rs. 4500 for the whole year.

- The total profit at the end of the year is Rs. 9900.

- B received a profit of Rs. 4400.

- Since profits are shared according to the time and amount invested, we can equate the ratio of their investments to the ratio of their profits.

- Let B join the business after x months. B's investment is then for (12 - x) months.

- Therefore, (4500 * 12) / (4800 * (12 - x)) = (9900 - 4400) / 4400

- Solving this equation, 54000 / (4800 * (12 - x)) = 5 / 4

- Simplifying gives: 5 * (12 - x) = 4 * 11.25

- 60 - 5x = 45

- 5x = 15

- x = 3

Correct Answer: 4) 3 months