The simple interest at $x$% for $x$ years will be ₹ $x$ on a sum of :

### Concept & Algebraic Substitution in Simple Interest The same standard formula applies even when the values are variables. We isolate the Principal ($P$): $$P = \frac{SI \times 100}{R \times T}$$ ### Step-by-Step Solution * Given Simple Interest, $SI = x$ * Given Rate, $R = x\%$ p.a. * Given Time, $T = x \text{ years}$ * Substitute these variable values into the formula: $P = \frac{x \times 100}{x \times x}$ * Cancel out the common $x$ from the numerator and denominator: $P = \frac{100}{x}$ ### Exam Strategy & Shortcut Whenever $SI$, $R$, and $T$ are all equal to the same variable $x$, the formula $P = \frac{SI \times 100}{R \times T}$ immediately simplifies to $\frac{100}{x}$ because one $x$ from the numerator ($SI$) cancels out one $x$ from the denominator ($R \times T$). ### Common Pitfall A common mistake is accidentally multiplying the terms to get $\frac{100}{x^2}$ instead of canceling the $x$ properly. ### Final Answer Therefore, the correct answer is **₹ $\left(\frac{100}{x}\right)$**.