A and B invest in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is ₹ 4,275 after the donation, what is the total profit?

Introduction / Context: This is the same structure as earlier: remove charity first, then divide the remainder using the investment ratio, equating A's portion to the given value.

Given Data / Assumptions:

• A : B = 3 : 2.
• Charity = 5% of total profit P.
• A's share after donation = ₹ 4,275.

Concept / Approach: A's portion = (3/5) * 0.95 * P = 0.57P. Set equal to 4,275 and solve for P.

Step-by-Step Solution: 0.57P = 4,275 ⇒ P = 4,275 / 0.57 = ₹ 7,500. Charity = 5% of 7,500 = ₹ 375; distributable = ₹ 7,125. A's share = 3/5 of 7,125 = ₹ 4,275 (checks).

Verification / Alternative check: B's share = 2/5 of 7,125 = ₹ 2,850; total after charity = 4,275 + 2,850 = 7,125; adding charity returns ₹ 7,500.

Why Other Options Are Wrong: They do not produce A's post-charity amount of ₹ 4,275 under the 3 : 2 split.

Common Pitfalls: Taking 3/5 of P directly or forgetting to subtract charity before splitting.

Final Answer: ₹ 7,500