Partnership profit handling with donation and reinvestment — Pankaj and Sushil invest in the ratio 3:5 for the same period. At year-end, 20% of total profit is donated to the AIDS Control Society of India; of the remaining 80%, 75% is reinvested and the balance (i.e., 25% of 80%) is divided as interest on capitals in the 3:5 ratio. If the difference in their distributed shares is ₹ 1200, find the total profit for the year.

Introduction / Context: This partnership problem tests layered profit treatment: a charitable donation, reinvestment, and then distribution of the remaining portion based on capital ratio. Only the finally distributed portion generates the ₹ 1200 difference between partners’ shares. We reverse the steps to retrieve the total annual profit.

Given Data / Assumptions:

• Investment ratio (Pankaj:Sushil) = 3:5.
• Donation = 20% of total profit.
• Of the remaining 80%, 75% is reinvested; 25% is distributed as interest on capitals.
• Difference in distributed shares = ₹ 1200.

Concept / Approach: Let total profit be P. The distributable part after donation and reinvestment is 25% of 80% of P = 0.20P. Shares are in 3:5. Compute the difference between 5/8 and 3/8 of 0.20P, set it equal to ₹ 1200, and solve for P.

Step-by-Step Solution:

Verification / Alternative check: Plugging back: D = 0.20 * 24000 = 4800. Shares: Pankaj 1800, Sushil 3000; difference = 1200 (matches).

Why Other Options Are Wrong: 18000 and 20000 do not produce a ₹ 1200 difference under the given proportions. “None of these” is unnecessary since 24000 fits exactly.

Common Pitfalls: Distributing the entire 80% instead of only 25% of it, or mistakenly applying the 3:5 split before donation/reinvestment deductions.

Final Answer: 24000