A and B invest in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share of the remainder is ₹855, what is the total profit?

Problem restatementA fixed 5% of the total profit P is donated. The remaining 95% is divided between A and B in the ratio 3 : 2, with A's portion equal to ₹855. Find P.

Given data

• Charity = 5% of P → distributable = 95% of P.
• A's share from distributable = (3/5) × 0.95P = ₹855.

Concept/ApproachSet up an equation for A's share and solve for P.

Step-by-step calculation (3/5) × 0.95P = 0.57P = 855 P = 855 ÷ 0.57 = ₹1,500

VerificationDistributable = 0.95 × 1,500 = ₹1,425. A's share = 3/5 × 1,425 = ₹855 (matches).

Common pitfalls

• Applying 5% charity after taking A's share instead of before.

Final Answer₹1,500