Profit split with partial equal division and interest on capital: Two partners invest ₹ 125000 and ₹ 85000. They agree that 60% of the profit is divided equally and the remaining 40% is distributed in the ratio of their capitals. If one partner receives ₹ 600 more than the other, find the total profit.

Introduction / Context:
This is a hybrid profit-sharing agreement: part equally, part proportional to capital (often called interest on capital). We use the difference between partners’ final receipts to back-solve the total profit.

Given Data / Assumptions:

• Capitals: 125000 and 85000 → ratio 25 : 17.
• 60% of profit split equally; 40% split in 25 : 17.
• Difference between partners’ totals = ₹ 600.

Concept / Approach:
Let total profit be P. Each gets 0.3P from the equal part. From the 40% part, the first gets 0.4P*(25/42), the second 0.4P*(17/42). The difference equals 0.4P*(8/42) = (1.6/21)P. Set this equal to ₹ 600 and solve for P.

Step-by-Step Solution:
Difference = 0.4P * (25−17)/42 = 0.4P * 8/42 = (1.6/21)P.(1.6/21)P = 600 ⇒ P = 600 * 21 / 1.6 = 600 * 13.125 = ₹ 7875.

Verification / Alternative check:
Compute the unequal portion: 0.4P = 3150. Shares in 25 : 17 are 1875 and 1275, difference 600. The equal portion is 0.6P = 4725 → 2362.5 each. Totals differ by exactly 600, confirming P = ₹ 7875.

Why Other Options Are Wrong:

• ₹ 8800, ₹ 8885, and ₹ 8995 do not satisfy the derived proportional difference.

Common Pitfalls:

• Mistaking 60% as per-head rather than equal split.
• Using 25 : 17 on the whole profit instead of only the 40% portion.

Final Answer:
₹ 7875