In a partnership business, Anand invests Rs. 22,500 and Deepak invests Rs. 35,000. Out of a total profit of Rs. 13,800, what is the share of Deepak in the profit?

Introduction / Context:
This is a standard aptitude question on partnership in which two people invest different amounts of capital in a business and share the profit in proportion to their investments. The aim is to calculate Deepak's share of the total profit of Rs. 13,800, given the amounts invested by Anand and Deepak.

Given Data / Assumptions:

• Anand invests Rs. 22,500 in the business.
• Deepak invests Rs. 35,000 in the business.
• The investment period for both partners is the same.
• Total profit at the end of the period is Rs. 13,800.
• Profit is shared in the ratio of their invested capitals.

Concept / Approach:
In partnership problems, when the time period of investment is the same, the profit is divided in the ratio of the invested capital amounts. First we find the ratio of Anand's and Deepak's investments. Then we divide the total profit in this ratio and calculate Deepak's part using the ratio method: partner share = total profit * partner ratio / sum of ratios.

Step-by-Step Solution:
Step 1: Write the investment amounts: Anand = 22,500 and Deepak = 35,000. Step 2: Find the ratio of their investments: 22,500 : 35,000. Step 3: Simplify this ratio by dividing both numbers by 2,500 to get 9 : 14. Step 4: The total number of parts in the ratio is 9 + 14 = 23. Step 5: Each part of the profit is equal to 13,800 / 23. Step 6: Deepak has 14 parts, so his share = 14 * (13,800 / 23) = 8,400. Step 7: Therefore, Deepak receives Rs. 8,400 from the total profit.

Verification / Alternative check:
We can verify by also calculating Anand's share. Anand has 9 parts, so his share is 9 * (13,800 / 23) = 5,400. Adding both shares, 5,400 + 8,400 = 13,800, which matches the total profit. This confirms that our ratio-based calculation is consistent and correct.

Why Other Options Are Wrong:
Options 8200, 8100 and 8000 do not satisfy the capital ratio 9 : 14 when combined with Anand's corresponding share. If Deepak received any of these amounts, Anand's share plus Deepak's share would either not add up to 13,800 or would not preserve the required ratio between their investments.

Common Pitfalls:
A common mistake is to subtract one investment from the other or to divide the profit directly by two without considering the ratio of capitals. Another frequent error is simplifying the ratio incorrectly or forgetting to add the ratio parts before distributing the profit. Always remember that profits in such partnership problems are shared in proportion to capital multiplied by time, and when time is equal, only capital matters.

Final Answer:
Deepak's share of the total profit is Rs. 8,400.