A starts a business with ₹ 10,000. After 4 months, B joins with ₹ 5,000. At the end of 12 months the total profit is ₹ 2,000. What is A’s share of the profit?

Introduction / Context:
In partnerships, profit shares are proportional to “capital × time.” Compute each partner’s capital-months, form the profit-share ratio, and apply it to the total profit.

Given Data / Assumptions:

• A invests ₹ 10,000 for 12 months.
• B invests ₹ 5,000 for 8 months (joins after 4 months).
• Total profit = ₹ 2,000.

Concept / Approach:
Capital-months: A = 10000 * 12; B = 5000 * 8. The ratio A : B determines the split of the profit.

Step-by-Step Solution:
A’s capital-months = 10000 * 12 = 120000B’s capital-months = 5000 * 8 = 40000A : B = 120000 : 40000 = 3 : 1A’s profit = (3/4) * 2000 = ₹ 1500

Verification / Alternative check:
B’s profit = (1/4) * 2000 = ₹ 500. Sum 1500 + 500 = 2000, matching the total profit.

Why Other Options Are Wrong:
800, 1000, 1200, and 1800 do not correspond to the 3 : 1 profit division based on capital-months.

Common Pitfalls:
Using months since start for both partners without adjusting for joining time; ignoring the time component leads to wrong shares.

Final Answer:
₹ 1500