Avinash, Manoj, and Arun invest in the ratio 3 : 2 : 5. At year-end, the profit is ₹45000, which is 15% of their total investment. How much did Manoj invest?

Introduction / Context:
The profit amount is given as a percentage of total investment. First convert profit to total investment, then distribute the total investment according to the given ratio to find each person’s capital.

Given Data / Assumptions:

• Investment ratio = 3 : 2 : 5.
• Profit = ₹45000 = 15% of total investment.
• Time assumed equal; ratio applies to investment amounts.

Concept / Approach:
If 15% equals ₹45000, then 100% (total investment) = 45000 / 0.15. After finding the total, compute the value per part and then Manoj’s amount (2 parts).

Step-by-Step Solution:
Total investment = 45000 / 0.15 = ₹300000Sum of ratio parts = 3 + 2 + 5 = 10Value of 1 part = 300000 / 10 = ₹30000Manoj’s investment = 2 parts = 2 * 30000 = ₹60000

Verification / Alternative check:
Avinash = 90000; Arun = 150000; sum = 90000 + 60000 + 150000 = 300000, consistent.

Why Other Options Are Wrong:
₹30000 is one part, not Manoj’s two parts. Other options do not align with the 3:2:5 structure.

Common Pitfalls:
Using the profit ratio as if it were the investment amounts. The question gives investment ratio explicitly.

Final Answer:
₹60000