P and Q are partners. P invests ₹ 8,000 for 8 months. Q stays in the business for 4 months and claims 2/7 of the total profit. How much money did Q invest?

Introduction / Context:
Profit shares are proportional to capital-time. Knowing Q's time and claimed fraction lets us solve for Q's capital by setting up a proportion equation.

Given Data / Assumptions:

• P: 8,000 for 8 months ⇒ weight = 64,000.
• Q: q for 4 months ⇒ weight = 4q.
• Q's profit fraction = 2/7.

Concept / Approach:
If Q's fraction is 2/7, then 4q / (64,000 + 4q) = 2/7. Solve for q.

Step-by-Step Solution:
7*(4q) = 2*(64,000 + 4q). 28q = 1,28,000 + 8q ⇒ 20q = 1,28,000 ⇒ q = ₹ 6,400.

Verification / Alternative check:
Weights become 64,000 and 25,600. Q's fraction = 25,600 / 89,600 = 0.2857… = 2/7. Correct.

Why Other Options Are Wrong:
Other amounts do not yield the exact 2/7 claim when substituted into the proportion.

Common Pitfalls:
Using 2/7 of 4 months instead of the fraction of total weight, or mixing up months and capital.

Final Answer:
₹ 6,400