Subodh invests Rs. 45,000. After 4 months, Nepal joins with Rs. 30,000. At year-end, the total profit is Rs. 13,000. What is the difference between their profit shares?

Introduction / Context:
Time-weighted capital determines shares when partners join later. We compute each partner’s capital * months, obtain the ratio, split the profit, and then find the difference in shares.

Given Data / Assumptions:

• Subodh: Rs. 45,000 invested for 12 months.
• Nepal: Rs. 30,000 invested after 4 months ⇒ for 8 months.
• Total profit = Rs. 13,000.

Concept / Approach:
Profit ratio = (capital * time). Then difference = (Subodh’s share − Nepal’s share) after distributing the total profit according to their parts.

Step-by-Step Solution:
Subodh weight = 45,000 * 12 = 540,000. Nepal weight = 30,000 * 8 = 240,000. Ratio = 540 : 240 = 9 : 4. Total parts = 13; Subodh’s share = (9/13) * 13,000 = Rs. 9,000. Nepal’s share = (4/13) * 13,000 = Rs. 4,000. Difference = 9,000 − 4,000 = Rs. 5,000.

Verification / Alternative check:
Shares 9,000 and 4,000 add to 13,000 and reflect the 9 : 4 ratio accurately.

Why Other Options Are Wrong:
Rs. 7,000, Rs. 3,000, and Rs. 9,000 do not match the computed Rs. 5,000 difference; hence “None of these” is correct.

Common Pitfalls:
Using 4 months instead of 8 months for Nepal, or forgetting to multiply capital by time in months before forming the ratio.

Final Answer:
None of these