Karim invests Rs. 30,000 for one year. What amount should Raunaq invest for one year so that the profit ratio (Karim : Raunaq) is 2 : 3?

Introduction / Context:
With equal time periods, profit shares are simply proportional to invested capital. We are given the desired profit ratio and Karim’s capital, and must find Raunaq’s capital accordingly.

Given Data / Assumptions:

• Karim: Rs. 30,000 for 1 year.
• Desired profit ratio Karim : Raunaq = 2 : 3.
• Time for both partners is equal, so ratio equals capitals.

Concept / Approach:
Set 30,000 : x = 2 : 3 and solve for x using cross-multiplication.

Step-by-Step Solution:
30,000 / x = 2 / 3. Cross-multiply: 2x = 90,000 ⇒ x = 45,000. Therefore, Raunaq must invest Rs. 45,000.

Verification / Alternative check:
Capitals 30,000 and 45,000 form the ratio 2 : 3; profits will follow the same ratio since time is identical.

Why Other Options Are Wrong:
Rs. 20,000, Rs. 40,000, and Rs. 18,000 do not yield the 2 : 3 ratio with 30,000.

Common Pitfalls:
Using 3 : 2 instead of 2 : 3 or forgetting that equal time periods eliminate the need for time weighting.

Final Answer:
Rs. 45000