K, L and M together start a business. K invests Rs. 6,000 for 5 months, L invests Rs. 3,600 for 6 months, and M invests Rs. 7,500 for 3 months. If the total profit at the end of the period is Rs. 7,410, what is the share of L in this profit?

Introduction / Context:
This question is a standard partnership problem in which three partners invest different amounts of money for different durations. To find the share of one partner in the total profit, we must calculate each partner's effective investment using the capital time concept and then distribute the profit in the same ratio.

Given Data / Assumptions:

• Partner K invests Rs. 6,000 for 5 months.
• Partner L invests Rs. 3,600 for 6 months.
• Partner M invests Rs. 7,500 for 3 months.
• Total profit at the end of the period is Rs. 7,410.
• Profit is shared in proportion to capital multiplied by time.

Concept / Approach:
The core principle is that if partners invest money for different time periods, their shares of profit are proportional to the product of capital and duration. We first compute each partner's capital time, then form their ratio and divide the total profit according to this ratio. Finally, we extract L's share.

Step-by-Step Solution:
Step 1: Compute K's capital time: 6,000 * 5 = 30,000 money months.Step 2: Compute L's capital time: 3,600 * 6 = 21,600 money months.Step 3: Compute M's capital time: 7,500 * 3 = 22,500 money months.Step 4: The ratio of K : L : M is 30,000 : 21,600 : 22,500.Step 5: The total of ratio units is 30,000 + 21,600 + 22,500 = 74,100.Step 6: Each money month unit corresponds to profit 7,410 / 74,100 = 0.1 rupee.Step 7: L's share of profit is 21,600 * 0.1 = Rs. 2,160.

Verification / Alternative check:
Check K's share: 30,000 * 0.1 = Rs. 3,000. M's share: 22,500 * 0.1 = Rs. 2,250. The total profit is 3,000 + 2,160 + 2,250 = Rs. 7,410, which matches the given total. Therefore, the calculation is consistent and confirms that L's share is correct.

Why Other Options Are Wrong:
Rs. 1,640 is too low and does not correspond to the ratio 30,000 : 21,600 : 22,500. Rs. 2,500 and Rs. 3,000 are larger than L's fair share based on her capital time; Rs. 3,000 actually corresponds to K's share. 'None of these' is incorrect because Rs. 2,160 is a valid option that exactly matches the partnership ratio.

Common Pitfalls:
Students sometimes mistakenly use only capital values and ignore time, or sum all investments and divide directly. Another error is to divide the total profit in the wrong proportion, such as using 6,000 : 3,600 : 7,500 instead of the correct money month values. Always multiply capital by time before forming the ratio for partnership questions.

Final Answer:
The correct share of L in the total profit is Rs. 2,160.