Let's solve this step by step.

Assumptions:

• Let the amount of money P invests initially be $x$.
• Q invests twice the amount of P, which is $2x$, after 6 months.
• R invests thrice the amount of P, which is $3x$, after 8 months.

Step 1: Calculate the time each partner's money is invested.

• P: P invests $x$ from the beginning for the whole year, i.e., for 12 months.
• Q: Q invests $2x$ after 6 months, so the money is invested for 6 months.
• R: R invests $3x$ after 8 months, so the money is invested for 4 months.

Step 2: Calculate the effective capital for each partner.

The effective capital is the product of the invested amount and the time it remains invested.

• For P: $x \times 12 = 12x$
• For Q: $2x \times 6 = 12x$
• For R: $3x \times 4 = 12x$

Step 3: Determine the ratio of their investments.

The total investment ratio is proportional to their effective capital contributions: $\text{Ratio of P:Q:R} = 12x : 12x : 12x = 1:1:1$

Step 4: Calculate Q's share of the profit.

Since the ratio of investments is $1:1:1$, the total profit will be divided equally among P, Q, and R.

The total profit is Rs. 9,000. Therefore, Q's share is: $\text{Q's Share} = \frac{9000}{3} = 3000 \text{ Rs.}$

Thus, Q's share of the profit is Rs. 3,000.

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Do you want any further details or have any questions?

Here are some related questions:

1. How is the effective capital ratio calculated in partnership?
2. How would the result change if R invested earlier than 8 months?
3. What would happen if P, Q, and R invested different amounts for the same time periods?
4. How is profit distributed in a partnership if no information on time or capital is provided?
5. What is the general formula for calculating profit share in a partnership?

Tip: In partnership problems, both the amount of investment and the time for which the investment is made are crucial in determining the profit share.