Simran invests Rs. 50,000 to start a software business. After 6 months, Nanda joins with Rs. 80,000. After 3 years, the profit is Rs. 24,500. What is Simran's share of the profit?

Problem restatement
Profits in a partnership are divided in proportion to (capital × time). Simran invests first; Nanda joins after 6 months. Compute time-weighted capitals and apportion the total profit.

Given data

• Simran's capital = Rs. 50,000 for 3 years.
• Nanda's capital = Rs. 80,000 for 2.5 years (joins after 6 months).
• Total profit = Rs. 24,500.

Concept/Approach
Use capital–month (or capital–year) products to get their profit-sharing ratio, then apply the ratio to the total profit.

Step-by-Step calculation
Simran's units = 50,000 × 3 = 150,000Nanda's units = 80,000 × 2.5 = 200,000Ratio (Simran : Nanda) = 150,000 : 200,000 = 3 : 4Total parts = 3 + 4 = 7Simran's share = (3/7) × 24,500 = 10,500

Verification/Alternative
If Nanda had also invested for 3 years, the ratio would be 5:8; reducing Nanda's time to 2.5 years scales her part to 4 and yields 3:4 overall—consistent.

Common pitfalls
Using plain capital ratio (50,000:80,000) without accounting for different investment durations.

Final Answer
Rs. 10,500