In a business partnership, A and B invest their capitals in the ratio 3 : 2. If 5% of the total profit is donated to charity and the share of A in the remaining profit is Rs. 855, what is the total profit earned by the business in that year?

Introduction / Context:
This is a standard partnership problem involving profit sharing and a deduction for charity. Questions of this type check whether you understand how total profit is adjusted after a certain percentage is taken out and how the remaining amount is divided in a given ratio among partners. You must translate the given information into simple percentage and ratio equations to find the total profit.

Given Data / Assumptions:
- A and B invest in the business in the ratio 3 : 2.
- 5 percent of the total profit is given to charity before distribution to partners.
- The share of A from the remaining profit is Rs. 855.
- We are asked to calculate the total profit of the business.

Concept / Approach:
First, let the total profit be P. A fixed percentage of this profit, namely 5 percent, is taken out as charity. The remaining 95 percent of P is then divided between A and B in the ratio 3 : 2. A receives three fifths of this remaining amount because the sum of the ratio parts is 3 + 2 = 5. By equating A's calculated share to the given amount of Rs. 855, we can solve for P.

Step-by-Step Solution:
Step 1: Let total profit be P.Step 2: Charity amount is 5 percent of P, which is (5 / 100) * P = 0.05 * P.Step 3: Remaining profit after charity is 95 percent of P, which is 0.95 * P.Step 4: This remaining profit is divided between A and B in the ratio 3 : 2. So A's share is (3 / (3 + 2)) * 0.95 * P = (3 / 5) * 0.95 * P.Step 5: Compute A's share as 0.57 * P. We are given that this equals Rs. 855. So 0.57 * P = 855.Step 6: Therefore P = 855 / 0.57. Since 57 * 15 = 855, P = 1500.

Verification / Alternative check:
We can confirm by reversing the steps. If total profit is Rs. 1500, then 5 percent charity is (5 / 100) * 1500 = Rs. 75. Remaining profit is 1500 - 75 = Rs. 1425. A's share should be three fifths of 1425. That is (3 / 5) * 1425 = 3 * 285 = 855, which matches the given information. Therefore the total profit value is correct.

Why Other Options Are Wrong:
If total profit were Rs. 500, 5 percent charity would be Rs. 25 and the remaining Rs. 475 would give A a share of (3 / 5) * 475 = Rs. 285, not 855. For Rs. 1000 total profit, A's share after 5 percent charity comes out to 570, which again does not match. For Rs. 2000, A would receive more than 855. Hence these options are inconsistent with the data provided.

Common Pitfalls:
A very common mistake is to directly divide 855 in the ratio 3 : 2 without first considering the 5 percent charity. Another error is to apply 5 percent on A's share instead of on the total profit. Some students also convert the ratio incorrectly, forgetting that A receives 3 out of 5 equal parts of the remaining profit. Keeping the order clear, first charity then ratio division, avoids these mistakes.

Final Answer:
The total profit earned by the business is Rs. 1500.