Target average return via a two-rate mix: A man invests ₹ 3000 at the rate of 5% per annum. How much additional money should he invest at the rate of 8% per annum so that his overall annual return works out to exactly 6% per annum on the combined investment?

Introduction / Context:
This is a classic weighted-average simple interest problem: combining two slices at different rates to hit a target blended rate across the total principal.

Given Data / Assumptions:

• First part P1 = ₹ 3000 at r1 = 5% p.a.
• Second part P2 = x at r2 = 8% p.a.
• Target blended rate R = 6% p.a. on P1 + P2.

Concept / Approach:
Total annual interest from both parts must equal 6% of the combined principal. Form a single linear equation in x and solve.

Step-by-Step Solution:
(0.05 * 3000 + 0.08 * x) / (3000 + x) = 0.06(150 + 0.08x) = 0.06(3000 + x) = 180 + 0.06x0.08x − 0.06x = 180 − 150 = 30 → 0.02x = 30 → x = ₹ 1500

Verification / Alternative check:
Interest: 5% of 3000 = 150; 8% of 1500 = 120. Total = 270. Combined principal = 4500. 270/4500 = 0.06 → 6%.

Why Other Options Are Wrong:
₹ 1200, ₹ 1300, ₹ 1000 or ₹ 2000 produce blended rates not equal to 6% when substituted in the equation.

Common Pitfalls:
Forgetting to divide by total principal or equating interest sums without normalizing by P1 + P2 for the blended rate.

Final Answer:
₹ 1500