Alok invests Rs. 75,000. After 3 months, Chandan joins with Rs. 60,000. If the annual profit is Rs. 16,000, what is Chandan’s share?

Introduction / Context:
Profit shares are proportional to capital * time. A later-joining partner contributes for fewer months, reducing his weighted share even with a sizable capital.

Given Data / Assumptions:

• Alok: Rs. 75,000 for 12 months.
• Chandan: Rs. 60,000 for 9 months (joined after 3 months).
• Total profit = Rs. 16,000.

Concept / Approach:
Compute weights: 75,000 * 12 and 60,000 * 9. Reduce the ratio, then split Rs. 16,000 accordingly to find Chandan’s share.

Step-by-Step Solution:
Alok weight = 900,000. Chandan weight = 540,000. Ratio = 900 : 540 = 5 : 3. Total parts = 8; Chandan’s share = (3/8) * 16,000 = Rs. 6,000.

Verification / Alternative check:
Alok’s share = (5/8) * 16,000 = Rs. 10,000. Sum = 16,000, consistent with the ratio 5 : 3.

Why Other Options Are Wrong:
Rs. 10,000 is Alok’s share. Rs. 8,000 and Rs. 4,500 do not match the 5 : 3 ratio split.

Common Pitfalls:
Using raw capitals without time weighting or miscounting the months for Chandan’s investment.

Final Answer:
Rs. 6000