Back-calculating a partner’s capital from a claimed profit share: A invests ₹ 16,000 for 8 months. B stays in the business for 4 months and claims 2/7 of the total profit. Find B’s capital.

Introduction / Context:
With two partners, profit shares are proportional to capital × time. If a partner’s profit fraction is known, we can set up a ratio equation between the two capital-time products and solve for the unknown capital directly.

Given Data / Assumptions:

• A capital = ₹ 16,000 for 8 months ⇒ A weight = 1,28,000.
• B time = 4 months; capital = y (unknown) ⇒ B weight = 4y.
• B’s profit fraction = 2/7 ⇒ A’s fraction = 5/7 ⇒ A : B = 5 : 2.

Concept / Approach:
Set the weight ratio equal to 5 : 2 and solve for y. This ensures the shares align with the claimed profit fraction exactly.

Step-by-Step Solution:

Verification / Alternative check:
B weight = 4 * 12,800 = 51,200; ratio 1,28,000 : 51,200 = 5 : 2 (divide by 25,600), matching the profit claim.

Why Other Options Are Wrong:
₹ 13,600, ₹ 11,900, ₹ 10,500, ₹ 14,000 do not maintain the 5 : 2 weight ratio with A’s 1,28,000 weight.

Common Pitfalls:
Using 2 : 5 instead of 5 : 2 for A : B, or forgetting to multiply capital by months to form weights.

Final Answer:
12800