Simple Interest – Feasibility check repeated at 8% for 6 years: The simple interest on a sum at 8% per annum for 6 years is claimed to be half the principal. Determine the sum or conclude feasibility.

Introduction / Context:
We test whether the given interest statement is compatible with simple-interest proportionality. If the computed interest fraction differs from the claim, no principal can satisfy the condition, and we cannot determine a unique sum.

Given Data / Assumptions:

• Rate r = 8% per annum
• Time t = 6 years
• Claim: simple interest equals half of the principal

Concept / Approach:
Use I = P * r * t / 100 and compare I / P to 1/2. The fraction depends only on r and t for simple interest, not on P.

Step-by-Step Solution:
I / P = (r * t) / 100 = (8 * 6) / 100 = 48 / 100 = 0.48The claim requires 0.50. Since 0.48 ≠ 0.50, the condition cannot be met by any principal.

Verification / Alternative check:
Try P = ₹ 6,000: I = 6,000 * 8 * 6 / 100 = ₹ 2,880 (48% of P), not half. The contradiction persists for all P values.

Why Other Options Are Wrong:
Numerical principal choices cannot resolve a percentage contradiction. “Not possible” is a reasonable description; within the provided set, the intended answer is “Data is inadequate” (no sum can be uniquely determined).

Common Pitfalls:
Confusing “half the amount” with “half the principal,” or overlooking that simple interest scales linearly with P, r, and t, not with arbitrary claims.

Final Answer:
Data is inadequate