Jayant invests Rs. 6,000 for 12 months. After 6 months, Madhu joins with Rs. 4,000 for the last 6 months. If the total profit is Rs. 5,200, what is Madhu’s share?

Introduction / Context:
When partners join at different times, use capital * time to determine profit shares. Here we compute Jayant’s and Madhu’s time-weighted capitals and then divide the profit accordingly.

Given Data / Assumptions:

• Jayant: Rs. 6,000 for 12 months.
• Madhu: Rs. 4,000 for 6 months.
• Total profit = Rs. 5,200.

Concept / Approach:
Profit share ratio = (6000 * 12) : (4000 * 6). Convert to simplest ratio and allocate the total profit by parts.

Step-by-Step Solution:
Jayant weight = 6,000 * 12 = 72,000. Madhu weight = 4,000 * 6 = 24,000. Ratio = 72,000 : 24,000 = 3 : 1. Total parts = 3 + 1 = 4; each part = 5,200 / 4 = 1,300. Madhu’s share = 1,300.

Verification / Alternative check:
Jayant’s share = 3 * 1,300 = 3,900; Madhu’s share = 1,300. Sum = 5,200, confirming the distribution.

Why Other Options Are Wrong:
2,080, 1,800, and 2,600 are inconsistent with the 3 : 1 time-weighted ratio.

Common Pitfalls:
Forgetting to multiply by months invested or mistakenly using raw capitals without time adjustment.

Final Answer:
Rs. 1300