Profit split with equal time but unequal capitals: P and Q invest ₹ 13,000 and ₹ 25,000, respectively, for 3 years. If the total profit is ₹ 76,000, what is Q’s share?

Introduction / Context:
When partners keep their investments for the same duration, profit splitting reduces to the ratio of capitals alone. We simply apply the capital ratio to the total profit to find each person’s share accurately and quickly.

Given Data / Assumptions:

• P capital = ₹ 13,000; Q capital = ₹ 25,000.
• Time = same for both (3 years), so it cancels in ratios.
• Total profit = ₹ 76,000.

Concept / Approach:
Profit share P : Q = 13,000 : 25,000 = 13 : 25. Q’s fraction of profit = 25 / (13 + 25) = 25/38. Multiply this fraction by the total profit to get Q’s amount.

Step-by-Step Solution:

Verification / Alternative check:
P share = 76,000 − 50,000 = ₹ 26,000, which matches 13/38 of the total profit, confirming correctness.

Why Other Options Are Wrong:
₹ 26,000 is P’s share; other options do not match the 13 : 25 capital split with a total of ₹ 76,000.

Common Pitfalls:
Forgetting to add ratio parts before division or attempting to use time weights even though the time is the same for both partners.

Final Answer:
₹ 50000