The simple interest at the rate of $p\%$ per annum for $p$ years will be ₹ $p$. Then, the principal is ________.
(A) ₹ $p$
(B) ₹ $100\,p$
(C) ₹ $\dfrac{100}{p^2}$
(D) ₹ $\dfrac{100}{p}$

Question

Accepted Answer

> [!TLDR]
> Put rate $=p\%$, time $=p$ years and $SI=upee p$ into the simple-interest formula and solve for the principal; the $p^2$ from rate×time cancels one $p$ from the interest, giving $P=\dfrac{100}{p}$.

### Step 1 — Write the simple-interest formula

$$SI = \frac{P 	imes R 	imes T}{100}$$

### Step 2 — Substitute the given data
Rate $R=p\%$, time $T=p$ years, and the interest is $SI=upee\,p$:

$$p = \frac{P 	imes p 	imes p}{100} = \frac{P\,p^{2}}{100}$$

### Step 3 — Solve for the principal $P$
Multiply both sides by $100$ and divide by $p^{2}$:

$$P = \frac{100\,p}{p^{2}} = \frac{100}{p}$$

**Why the other options are wrong:** (A) ₹$p$ ignores the formula entirely; (B) ₹$100p$ forgets to divide by $p^{2}$; (C) ₹$\dfrac{100}{p^{2}}$ cancels the $p$ in the interest twice instead of once. …

Simple Interest

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Step 1 — Write the simple-interest formula

Step 2 — Substitute the given data

Step 3 — Solve for the principal $P$

Step 1 — Write the simple-interest formula

Step 2 — Substitute the given data

Step 3 — Solve for the principal PPP

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Step 3 — Solve for the principal $P$

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