A and B invest in a business in the ratio 2 : 5. Fifty percent of the total profit is donated to charity, and the remaining 50 percent is shared between A and B according to their investment ratio. If A's share of the profit is Rs. 3.6 lakhs, what is the total profit in lakhs?

Introduction / Context:
This partnership question involves both a charitable deduction and a profit division based on an investment ratio. A portion of the total profit goes to charity, and the rest is divided between two partners in a specified ratio. We are given A's final share and must find the original total profit of the business in lakhs.

Given Data / Assumptions:

• Investment ratio of A : B is 2 : 5.
• Fifty percent of the total profit goes to charity.
• The remaining fifty percent is divided between A and B according to the ratio 2 : 5.
• A's share of profit is Rs. 3.6 lakhs.
• We are asked for the total profit in lakhs.

Concept / Approach:
Let the total profit be P lakhs. Then 50 percent of P, that is P/2, goes to charity. The remaining P/2 is shared by A and B in the ratio 2 : 5. A's share is therefore a specific fraction of the total profit. By equating that fraction to the given 3.6 lakhs, we can solve for P. This method uses proportional reasoning and basic fraction operations.

Step-by-Step Solution:
Step 1: Let total profit be P lakhs.Step 2: Half of the profit, P/2, is donated to charity.Step 3: The remaining profit P/2 is shared between A and B in the ratio 2 : 5.Step 4: Total ratio parts for A and B are 2 + 5 = 7.Step 5: A's share from the remaining profit is (2/7) of P/2.Step 6: So A's share = (2/7) * (P/2) = (1/7) * P.Step 7: We are told A's share is 3.6 lakhs, so (1/7) * P = 3.6.Step 8: Multiply both sides by 7 to get P = 3.6 * 7 = 25.2 lakhs.

Verification / Alternative check:
If total profit is 25.2 lakhs, charity receives half, that is 12.6 lakhs. The remaining 12.6 lakhs is shared between A and B in the ratio 2 : 5. A's share is (2/7) * 12.6 = 3.6 lakhs, which matches the value given in the question. This confirms that the computed total profit is consistent with all conditions.

Why Other Options Are Wrong:
If total profit were 12.6 lakhs, A's share would be only (1/7) * 12.6 = 1.8 lakhs. If it were 37.8 lakhs, A's share would be 37.8 / 7 ≈ 5.4 lakhs. For 16.8 lakhs, A's share would be 2.4 lakhs. None of these values match the given share of 3.6 lakhs, so they are incorrect. 'None of these' is not correct because 25.2 lakhs is exactly the required total profit.

Common Pitfalls:
Some candidates forget that A receives his portion only from the remaining half of the profit after charity, not from the entire profit. Others mistakenly divide A's share by 2 or 5 directly without forming the correct fraction. Carefully identifying the portion of the total profit that is available for sharing is crucial in such questions.

Final Answer:
The total profit earned by the business is 25.2 lakhs.