Three partners invest Rs. 27,000, Rs. 81,000, and Rs. 72,000 respectively. If Ram’s profit share is Rs. 36,000 after one year, what is the total profit?

Introduction / Context:
When all partners invest for the same time, profits are divided in the ratio of their capitals. Given Ram’s share and his capital, we back-calculate the total profit.

Given Data / Assumptions:

• Dilip = Rs. 27,000; Ram = Rs. 81,000; Amar = Rs. 72,000.
• Time = 1 year for all.
• Ram’s profit = Rs. 36,000.

Concept / Approach:
Ram’s fraction of profit = Ram’s capital / total capital. Then total profit = Ram’s share / Ram’s fraction.

Step-by-Step Solution:
Total capital = 27,000 + 81,000 + 72,000 = 180,000. Ram’s fraction = 81,000 / 180,000 = 9 / 20 = 0.45. Total profit = 36,000 / 0.45 = Rs. 80,000.

Verification / Alternative check:
Check shares with total Rs. 80,000: Ram gets 0.45 * 80,000 = Rs. 36,000, matching the given. Others would get Rs. 12,000 and Rs. 32,000 respectively, summing to Rs. 80,000.

Why Other Options Are Wrong:
Rs. 108,000 and Rs. 16,000 do not satisfy Ram’s 45% share equalling Rs. 36,000. “None of these” is incorrect because Rs. 80,000 is valid.

Common Pitfalls:
Dividing by the wrong total or miscomputing the fractional share. Ensure the ratio uses the sum of all capitals for the same time period.

Final Answer:
Rs. 80,000