Calculating Partnership Profit Share

This problem involves calculating profit distribution in a business partnership where partners invest different amounts for different durations. The profit share is proportional to the product of the investment amount and the duration of the investment.

Investment and Duration Analysis

First, let's list the investment details for each partner (A, B, and C) for the entire year (12 months):

• A's Investment: Rs. 75,000 for 12 months.
• B's Investment: Rs. 45,000 for 12 months.
• C's Investment: Rs. 60,000 for 9 months (since C joined after 3 months).

Calculating Effective Investment Ratio

To find the profit-sharing ratio, we calculate the 'effective investment' for each partner by multiplying their investment amount by the duration in months:

• A's Effective Investment = $75,000 \times 12 = 900,000$
• B's Effective Investment = $45,000 \times 12 = 540,000$
• C's Effective Investment = $60,000 \times 9 = 540,000$

The ratio of their effective investments is:

A : B : C = $900,000 : 540,000 : 540,000$

Simplifying this ratio by dividing all parts by their greatest common divisor (180,000):

A : B : C = $5 : 3 : 3$

Distributing the Profit

The total profit is Rs. 40,000. This profit needs to be distributed among A, B, and C according to the ratio $5:3:3$.

First, find the sum of the ratio parts:

Total Ratio Parts = $5 + 3 + 3 = 11$

Now, calculate C's share of the profit. C has 3 parts out of the total 11 parts.

C's Share = $\frac{\text{C's Ratio Part}}{\text{Total Ratio Parts}} \times \text{Total Profit}$

C's Share = $\frac{3}{11} \times 40,000$

C's Share = $\frac{120,000}{11}$

C's Share $\approx 10,909.09$

Therefore, C's share in the profit is approximately Rs. 10,909.