Profit share with unequal times (insufficient timing data): Ramesh and Priya invest ₹ 5,100 and ₹ 6,600 respectively for different, unknown durations. If the total profit is ₹ 5,460, determine Ramesh’s profit or conclude if the data are insufficient.

Introduction / Context:
In partnerships, profit is split in proportion to capital × time. When investment amounts are known but the investment periods are not fully specified, the share cannot be uniquely determined. This question tests whether you recognize when information is insufficient rather than forcing a calculation with assumptions not given in the problem.

Given Data / Assumptions:

• Ramesh’s capital = ₹ 5,100 for an unknown number of months.
• Priya’s capital = ₹ 6,600 for an unknown number of months (not equal to Ramesh’s time).
• Total profit = ₹ 5,460; no further timing relations are provided.

Concept / Approach:
Profit share ∝ capital * time. Without knowing both partners’ times (or at least their ratio), we cannot form a unique ratio of capital × time and hence cannot split the profit uniquely.

Step-by-Step Solution:

Verification / Alternative check:
Suppose t1 = t2; then the ratio would be 51 : 66. But if t2 = 2t1, the ratio becomes 51 : 132, giving a very different split. Hence, more information is needed.

Why Other Options Are Wrong:
The numeric options assume specific time relations not provided; selecting any fixed amount would be guesswork and not supported by the data.

Common Pitfalls:
Assuming equal times implicitly; or using only capital amounts to split the profit even when the problem explicitly says times differ.

Final Answer:
Data inadequate