Simple Interest – Compute 6-month interest after back-finding principal: A sum amounts to ₹ 2,240 at 4% per annum simple interest in 3 years. Find the interest on the same principal for 6 months at 3.5% per annum.

Introduction / Context:
This problem requires back-calculating the principal from a given amount under simple interest and then using that principal to find interest for a different time and rate. The linear nature of simple interest keeps calculations direct and proportional.

Given Data / Assumptions:

• A = ₹ 2,240 after 3 years at 4% per annum
• Simple interest relation: A = P + I and I = P * r * t / 100
• We need 6-month interest (t = 0.5 year) at 3.5% per annum on the same P

Concept / Approach:
First find P from A = P(1 + r * t / 100). Then compute I for the new t and r with I = P * r * t / 100.

Step-by-Step Solution:
A = P(1 + 4 * 3 / 100) = P(1 + 0.12) = 1.12PSo P = 2,240 / 1.12 = 2,000For 6 months at 3.5%: I = 2,000 * 3.5 * 0.5 / 100 = 35

Verification / Alternative check:
Compute the original 3-year interest at 4%: I = 2,000 * 4 * 3 / 100 = 240, amount = 2,240 as given. The interim calculation of P = ₹ 2,000 is confirmed.

Why Other Options Are Wrong:
₹ 30 and ₹ 25 understate the half-year interest; ₹ 50 and ₹ 150 overstate it for the specified rate and principal.

Common Pitfalls:
Misreading 6 months as 6 years or as 1 month, and mixing compound interest with simple interest, can distort results. Ensure time is in years for the formula.

Final Answer:
₹ 35