Simple Interest – Symbolic rate/time: find the sum that yields interest Rs x: At x% simple interest for x years, the interest equals Rs x. On what principal will this occur?

Introduction / Context:
This algebraic simple-interest question uses a symbolic percentage x% for a duration of x years and states that the resulting interest equals Rs x. We must infer the principal that makes the simple-interest formula produce that exact interest.

Given Data / Assumptions:

• Rate r = x% per annum
• Time t = x years
• Interest I = Rs x
• Simple interest relation: I = P * r * t / 100

Concept / Approach:
Substitute r and t into the formula and solve for P in terms of x. Keep x as a positive real to ensure meaningful financial interpretation.

Step-by-Step Solution:
I = P * x * x / 100 = P * x^2 / 100Given I = x ⇒ x = P * x^2 / 100Solve for P: P = 100 / x

Verification / Alternative check:
Plug P = 100 / x into I: I = (100 / x) * x^2 / 100 = x, which matches the given interest exactly.

Why Other Options Are Wrong:
Rs x and Rs 100x scale incorrectly with x; Rs (100/x^2) and Rs (x/100) produce wrong magnitudes when substituted back into I = P * x^2 / 100.

Common Pitfalls:
Dropping the 100 in the denominator or misinterpreting x% as x can produce quadratic or linear errors. Keep the percent handling consistent.

Final Answer:
Rs (100/x)