Simple Interest – Check feasibility when interest equals half the sum: The simple interest on a sum at 9% per annum for 5 years is stated to be half the principal. Determine the sum or conclude if the data are not feasible.

Introduction / Context:
Sometimes a simple-interest statement contradicts the formula, indicating that no real principal can satisfy the given relation. We must compare the proportional interest implied by the rate and time against the claimed fraction of the principal.

Given Data / Assumptions:

• Rate r = 9% per annum
• Time t = 5 years
• Claim: simple interest equals half of the principal

Concept / Approach:
For simple interest, I = P * r * t / 100. Compute the actual fraction of P produced by the given r and t, then compare with the claim of 1/2 P.

Step-by-Step Solution:
I / P = (r * t) / 100 = (9 * 5) / 100 = 45 / 100 = 0.45The claim requires I / P = 0.50Since 0.45 ≠ 0.50, no principal P can satisfy both the formula and the claim simultaneously.

Verification / Alternative check:
Pick any P (e.g., ₹ 5,000): I = 5,000 * 9 * 5 / 100 = ₹ 2,250, which is 45% of P, not 50%. The mismatch is independent of P.

Why Other Options Are Wrong:
Specific rupee values (₹ 5,800, ₹ 5,000, ₹ 7,000) cannot repair a percentage inconsistency. The outcome does not depend on P. “Not possible” conveys infeasibility; “Data is inadequate” is the intended pick here since no sum can be determined from inconsistent data.

Common Pitfalls:
Mistaking amount for interest or assuming compound interest when the prompt specifies simple interest can mask such contradictions.

Final Answer:
Data is inadequate