Simran starts a software business by investing Rs. 50,000. After 6 months, Nanda joins the business with a capital of Rs. 80,000. After 3 years from the start, the total profit is Rs. 24,500. What is Simran's share in this profit?

Introduction / Context:
This is a common partnership question where one partner starts a business and another joins later with a different capital amount. Profit must be shared in proportion to the product of capital and time. We are required to find Simran's share of the total profit after 3 years, given the capital amounts and the joining time of Nanda.

Given Data / Assumptions:

• Simran invests Rs. 50,000 at the beginning of the business.
• Nanda joins after 6 months with a capital of Rs. 80,000.
• Total duration from the start until profit calculation is 3 years, that is, 36 months.
• Thus Simran's capital is invested for 36 months.
• Nanda's capital is invested for 36 - 6 = 30 months.
• Total profit at the end of 3 years is Rs. 24,500.
• Profit is shared according to capital * time.

Concept / Approach:
When partners join at different times, we compute effective investment as capital multiplied by the number of months for which it is invested. These effective investments give the ratio for profit sharing. Once the ratio is obtained, we can calculate each partner's profit share by applying the ratio to the total profit.

Step-by-Step Solution:
Step 1: Effective investment of Simran = 50,000 * 36 = 18,00,000 rupee months. Step 2: Effective investment of Nanda = 80,000 * 30 = 24,00,000 rupee months. Step 3: Write the ratio of their effective investments: Simran : Nanda = 18,00,000 : 24,00,000. Step 4: Simplify this ratio by dividing by 6,00,000. This gives Simran : Nanda = 3 : 4. Step 5: Total ratio parts = 3 + 4 = 7. Step 6: Each ratio part of the profit = total profit / total parts = 24,500 / 7. Step 7: Compute Simran's share = 3 * (24,500 / 7) = 73,500 / 7 = Rs. 10,500. Step 8: Nanda's share would be 4 * (24,500 / 7) = 98,000 / 7 = Rs. 14,000.

Verification / Alternative check:
Add the calculated shares to verify. Simran gets Rs. 10,500 and Nanda gets Rs. 14,000. The total is 10,500 + 14,000 = 24,500, which matches the given total profit. This confirms that the ratio 3 : 4 and the resulting individual shares are correct based on the effective investments.

Why Other Options Are Wrong:
The alternative values 10,110, 12,000 and 13,000 do not correspond to a clean 3 : 4 ratio when combined with Nanda's implied share from the remaining profit. For example, if Simran received Rs. 12,000, Nanda would get 12,500 and the ratio would deviate from 3 : 4. Hence these options are inconsistent with the capital and time contributions.

Common Pitfalls:
Many learners mistakenly think that profit should be shared directly in the ratio 50,000 : 80,000 without considering the time difference. Another mistake is to assume the business lasted only 1 year instead of 3 years, which changes the effective investment calculation. Always multiply the capital by the exact duration in months before forming the ratio.

Final Answer:
Simran's share of the profit is Rs. 10,500.