A starts a taxi service by investing Rs. 25 lakhs. After 3 months, B joins the business by investing Rs. 40 lakhs, and 4 months after B joins (that is, after a total of 7 months from the start), C also joins by investing Rs. 50 lakhs. One year after A started the business, the total profit is Rs. 2,73,000. What is C's share of this profit, in rupees?

Introduction / Context:
This is a classic partnership problem with unequal joining times and unequal capital contributions. The partners A, B and C invest different amounts and join the business at different times. Because profit is proportional to both the amount of capital invested and the duration of the investment, we must compute effective contributions in money-time units. The question asks for C's share of the total profit earned over one year from the start of the business.

Given Data / Assumptions:
- A invests Rs. 25 lakhs from the beginning and remains for 12 months.- B joins after 3 months with Rs. 40 lakhs and remains until the end of the year.- C joins 4 months after B, which is 7 months after A started, with Rs. 50 lakhs and remains until the end of the year.- Total time considered is 12 months from A's start.- Total profit at the end of the year is Rs. 2,73,000.- We are required to find C's share of this profit.

Concept / Approach:
The key concept is capital-time weighting. Profit share is proportional to capital * time (for example, rupees multiplied by months). For each partner, we compute the product of their capital and the number of months that capital remained invested. The ratio of these products across all partners gives the ratio in which profit is divided. Then, we multiply the total profit by C's fraction of the total ratio to find C's share.

Step-by-Step Solution:
Step 1: Determine the time each partner's capital is invested.- A: invests for the full 12 months.- B: joins after 3 months, so invests for 12 - 3 = 9 months.- C: joins 4 months after B, i.e., after 7 months from start, so invests for 12 - 7 = 5 months.Step 2: Compute money-time units (capital * months).- A: 25 lakhs * 12 = 300 lakh-months.- B: 40 lakhs * 9 = 360 lakh-months.- C: 50 lakhs * 5 = 250 lakh-months.Step 3: Profit sharing ratio = 300 : 360 : 250.Step 4: Simplify the ratio by dividing by 10: 30 : 36 : 25.Step 5: Total parts = 30 + 36 + 25 = 91.Step 6: C's share fraction = 25 / 91.Step 7: Total profit = Rs. 2,73,000. So C's profit share = (25 / 91) * 2,73,000.Step 8: Compute (25 / 91) * 2,73,000 = 2,73,000 * 25 / 91.Step 9: 2,73,000 / 91 = 3,000. Thus C's share = 3,000 * 25 = Rs. 75,000.

Verification / Alternative check:
Compute A and B shares to ensure the total adds up.Each part of profit = 2,73,000 / 91 = 3,000.A's share = 30 * 3,000 = Rs. 90,000.B's share = 36 * 3,000 = Rs. 1,08,000.C's share = 25 * 3,000 = Rs. 75,000.Total = 90,000 + 1,08,000 + 75,000 = 2,73,000, which matches the given profit, confirming the answer.

Why Other Options Are Wrong:
- 100000: Larger than C's actual share; would require C to have a bigger ratio than 25/91.- 125000: Implies C gets nearly half the total profit, inconsistent with the calculated ratio.- 150000: Equal to more than half of the total profit, which is impossible given three partners with substantial contributions.

Common Pitfalls:
- Ignoring the different joining times and simply using the capital ratio 25 : 40 : 50.- Mixing up months and years, or miscalculating the duration each partner stays in the business.- Not simplifying the ratio correctly and making arithmetic mistakes while finding C's share.- Applying percentage ideas instead of the precise capital-time multiplication method, which is the correct approach for partnership timing questions.

Final Answer:
C's share of the profit is Rs. 75,000.