Sanjay and Komal each invest ₹ 15,000 to start a business. After 8 months, Komal withdraws ₹ 10,000, leaving ₹ 5,000 invested for the remaining 4 months. If the annual profit is ₹ 32,000, what is Sanjay's share?

Introduction / Context: When partners change their capital mid-year, profit shares must reflect capital-time products (capital multiplied by months invested). This ensures fairness based on both amount and duration.

Given Data / Assumptions:

• Sanjay: ₹ 15,000 for 12 months.
• Komal: ₹ 15,000 for 8 months, then ₹ 5,000 for 4 months.
• Total profit = ₹ 32,000.

Concept / Approach: Compute each partner's capital-time weight and divide the profit proportionally.

Step-by-Step Solution: Sanjay's weight = 15,000 * 12 = 180,000. Komal's weight = (15,000 * 8) + (5,000 * 4) = 120,000 + 20,000 = 140,000. Ratio = 180,000 : 140,000 = 18 : 14 = 9 : 7. Total parts = 16; Sanjay's fraction = 9/16. Sanjay's share = (9/16) * 32,000 = ₹ 18,000.

Verification / Alternative check: Komal's share would be 7/16 of 32,000 = ₹ 14,000. The two shares sum to ₹ 32,000, consistent with the total profit.

Why Other Options Are Wrong: ₹ 18,500, ₹ 17,000, and ₹ 16,500 do not fit the 9 : 7 split; ₹ 16,000 corresponds to an 8 : 8 equal split, which is not the case.

Common Pitfalls: Ignoring Komal's changed capital in the last four months or dividing the profit only by the initial ratio.

Final Answer: ₹ 18,000