Out of Rs. 7000, part is lent at 6% p.a. and the remainder at 4% p.a. If the total simple interest in 5 years is Rs. 1600, find the principal amount that was lent at 6% p.a.

Introduction / Context:
This problem checks understanding of simple interest with different interest rates applied to parts of a single principal. We are to determine how much of the total was placed at the higher rate given the total interest after a fixed time.

Given Data / Assumptions:

• Total principal = Rs. 7000.
• Rate 1 = 6% p.a. for x rupees.
• Rate 2 = 4% p.a. for the remainder (7000 − x).
• Time = 5 years; total interest = Rs. 1600.

Concept / Approach:
Simple interest formula: SI = P * r * t (with r in decimal per year). Sum interests from both portions and equate to the given total to solve for x, the amount at 6%.

Step-by-Step Solution:
Interest from 6% part = x * 0.06 * 5 = 0.30x. Interest from 4% part = (7000 − x) * 0.04 * 5 = 0.20(7000 − x) = 1400 − 0.20x. Total SI = 0.30x + (1400 − 0.20x) = 1400 + 0.10x. Set equal to 1600 ⇒ 1400 + 0.10x = 1600 ⇒ 0.10x = 200 ⇒ x = 2000.

Verification / Alternative check:
Compute SI: 2000 at 6% for 5 years = 600; 5000 at 4% for 5 years = 1000; total = 1600, matching the given sum.

Why Other Options Are Wrong:
Rs. 5000 and Rs. 3500 produce total SI values different from Rs. 1600; “None of these” is unnecessary because Rs. 2000 satisfies perfectly.

Common Pitfalls:
Using 6% of total instead of isolating the variable portion or forgetting to multiply by time for simple interest. Keep r as a decimal (e.g., 6% = 0.06).

Final Answer:
Rs. 2000