Gopal invests Rs. 3,000. After 6 months, Dinesh joins with Rs. 2,000. If the total profit at year-end is Rs. 2,600, what is Dinesh’s share?

Introduction / Context:
A partner joining halfway contributes for fewer months. Profit shares must reflect capital * time. We compute each partner’s weighted share and then apply it to the total profit.

Given Data / Assumptions:

• Gopal: Rs. 3,000 for 12 months.
• Dinesh: Rs. 2,000 for 6 months.
• Total profit = Rs. 2,600.

Concept / Approach:
Find the ratio (3,000 * 12) : (2,000 * 6) and then allocate Rs. 2,600 accordingly to obtain Dinesh’s share.

Step-by-Step Solution:
Gopal weight = 36,000. Dinesh weight = 12,000. Ratio = 3 : 1. Dinesh’s share = (1/4) * 2,600 = Rs. 650.

Verification / Alternative check:
Gopal’s share = 1,950; Dinesh’s = 650; sum to 2,600 and respect the 3 : 1 ratio.

Why Other Options Are Wrong:
Rs. 1,733 and Rs. 1,950 are not Dinesh’s share; Rs. 866 is not a clean quarter of 2,600.

Common Pitfalls:
Forgetting to weight by time or miscounting months. Always multiply capital by months invested before forming the ratio.

Final Answer:
Rs. 650