Rakesh, Dinesh, and Mahesh start a partnership business by investing ₹5000, ₹8000, and ₹12000 respectively. At the end of one year the total profit is ₹12500. Based strictly on capital–time proportionality (equal time), what is Dinesh’s share of the profit?

Introduction / Context:
This problem tests basic partnership theory. When partners invest for the same duration, the profit is divided in proportion to their invested capitals. No salary or interest is mentioned, so only capital matters.

Given Data / Assumptions:

• Investments: Rakesh = ₹5000, Dinesh = ₹8000, Mahesh = ₹12000.
• Time = 1 year for all (equal).
• Total profit = ₹12500.
• No other adjustments such as interest on capital or drawings.

Concept / Approach:
With equal time, profit share ∝ capital. Compute the investment ratio, convert to parts, and multiply Dinesh’s fraction by total profit.

Step-by-Step Solution:
Capital ratio = 5000 : 8000 : 12000 = 5 : 8 : 12Sum of parts = 5 + 8 + 12 = 25Dinesh’s fraction = 8/25Dinesh’s share = 12500 * (8/25) = 12500 * 0.32 = ₹4000

Verification / Alternative check:
Rakesh’s share = 12500*(5/25)=₹2500; Mahesh’s share = 12500*(12/25)=₹6000; total = 2500+4000+6000 = ₹12500, consistent.

Why Other Options Are Wrong:
₹4500, ₹6000, and ₹7500 correspond to different fractions (9/25, 12/25, 15/25) and do not match the 8-part share. ₹3200 implies 8/31.25 parts, which is not the given ratio.

Common Pitfalls:
Dividing profit equally or taking simple arithmetic mean of capitals. Always use proportional allocation to capital when times are equal.

Final Answer:
₹4000