Monoj and Ramesh earn a total profit of Rs. 9000 in one year, of which Monoj’s share is Rs. 6000. Monoj invested Rs. 20,000 for 6 months, while Ramesh invested his amount for the whole year. What amount did Ramesh invest?

Introduction / Context:
Profits divide in the ratio of capital × time. The profit split 6000 : 3000 = 2 : 1 gives the ratio of their capital-months. Use the known time spans to deduce Ramesh’s capital.

Given Data / Assumptions:

• Monoj profit = Rs. 6000, Ramesh profit = Rs. 3000 → ratio 2 : 1.
• Monoj capital × time = 20000 * 6 months = 120000 cap-months.
• Ramesh invests for 12 months with unknown capital R.

Concept / Approach:
Set capital-months ratio equal to 2 : 1 and solve for R. That directly yields R’s invested capital because his time is known.

Step-by-Step Solution:
Monoj : Ramesh (cap-months) = 120000 : 12R = 2 : 1Cross-multiply: 120000 * 1 = 2 * 12R ⇒ 120000 = 24RR = 120000 / 24 = Rs. 5000

Verification / Alternative check:
Ramesh cap-months = 5000 * 12 = 60000; 120000 : 60000 = 2 : 1, matching the profit split.

Why Other Options Are Wrong:
They imply cap-month ratios different from 2 : 1 under the given time spans.

Common Pitfalls:
Forgetting to multiply capital by months; comparing 20000 to R directly would be incorrect.

Final Answer:
Rs. 5000