A invests Rs. 8000 at the start. After 3 months, B joins with Rs. 5000. If the total profit at year-end is Rs. 2350, by how much does A’s share exceed B’s share?

Introduction / Context:
Compute the capital-months for each partner, convert to parts, and then multiply by the per-part profit to find each share. The difference asked is A’s share minus B’s share.

Given Data / Assumptions:

• A: 8000 for 12 months → 96000 units.
• B: 5000 for 9 months → 45000 units.
• Total profit = Rs. 2350.

Concept / Approach:
Profit per unit part = total profit / total units in “k-part” form. Since 96000 : 45000 reduces to 32 : 15, there are 47 parts in total. Each part equals 2350/47.

Step-by-Step Solution:
A : B = 96000 : 45000 = 32 : 15Total parts = 32 + 15 = 47Per part = 2350 / 47 = Rs. 50A’s share = 32 * 50 = Rs. 1600B’s share = 15 * 50 = Rs. 750Difference = 1600 − 750 = Rs. 850

Verification / Alternative check:
Sum shares = 1600 + 750 = 2350, matching the given profit.

Why Other Options Are Wrong:
600, 800, and 400 do not equal the computed gap from the exact 32:15 split.

Common Pitfalls:
Dividing profit directly in the ratio 8000:5000 without considering B’s late entry.

Final Answer:
Rs. 850