Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the rate of interest p.c.p.a.? (Bank P.O. 2009) I. I.An amount doubles itself at simple interest in 10 years. II. Difference between the compound interest and simple interest on an amount of ₹ 15000 in 2 years is ₹ 150. III. The compound interest accrued in 8 years is more than the principal.

### Concept & Isolating the Interest Rate We need to check which statement(s) provide enough mathematical data to form a complete equation to solve for the rate of interest ($R$). ### Step-by-Step Solution 1. **Evaluate Statement I:** The amount doubles itself at simple interest in 10 years. This implies $SI = P$. Formula: $P = \frac{P \times R \times 10}{100} \Rightarrow R = 10\%$. Statement I alone is sufficient. 2. **Evaluate Statement II:** The difference between CI and SI on ₹ 15000 for 2 years is ₹ 150. Formula for 2 years difference is $P(\frac{R}{100})^2 = \text{Difference}$. Substituting the given values: $15000(\frac{R}{100})^2 = 150$ $(\frac{R}{100})^2 = \frac{150}{15000} = \frac{1}{100}$ $\frac{R}{100} = \frac{1}{10} \Rightarrow R = 10\%$. Statement II alone is sufficient. 3. **Evaluate Statement III:** This gives an inequality (CI > Principal after 8 years). An inequality provides a range for the rate, not an exact discrete value. Insufficient. 4. Since both I and II independently provide the exact rate, either one alone is sufficient. ### Exam Strategy & Shortcut Recognize standard formulas immediately. Statement I is the classic simple interest doubling rule ($R = \frac{100}{T}$). Statement II provides all variables ($P$, Time, Difference) except $R$ for the standard 2-year difference equation. Both clearly form one-variable equations. ### Common Pitfall Trying to calculate exact threshold values for Statement III or combining it unnecessarily when Statements I and II already provide absolute, definitive answers on their own. ### Final Answer Therefore, the correct answer is **Only either I or II**.