Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the rate of interest p.c.p.a.? (Bank P.O., 2009) I. The amount doubles itself in 10 years. II. The simple interest accrued in 5 years is ₹ 5000.

### Concept & Rate of Interest from Multipliers When a principal sum becomes $n$ times itself over a period of $T$ years at Simple Interest, the interest earned is $(n-1)$ times the principal. This allows us to find the rate ($R$) directly without needing the actual monetary value of the principal. $$R = \frac{(n - 1) \times 100}{T}$$ ### Step-by-Step Solution * **From the Question:** We are asked to determine the rate of interest ($R$). * **Analyze Statement I:** The amount doubles itself in 10 years. This means $Amount = 2P$, so the Simple Interest $SI = Amount - P = 2P - P = P$. * Substituting into the SI formula: $P = \frac{P \times R \times 10}{100}$. * The variable $P$ cancels out: $1 = \frac{10R}{100} \Rightarrow R = 10\%$. * Since we can find a unique value for $R$ using only Statement I, it is sufficient. * **Analyze Statement II:** The simple interest ($SI$) is ₹ 5000 for $T = 5$ years. We do not have the principal sum ($P$), so we are left with two unknowns in the formula ($P$ and $R$). Statement II alone is insufficient. ### Exam Strategy & Shortcut Memorize the "doubling" shortcut for simple interest: If a sum doubles, the interest equals the principal ($100\%$). Simply divide $100$ by the number of years to get the rate. $100 / 10 = 10\%$. No complex algebra is needed. ### Common Pitfall A common trap is thinking you must combine both statements to find the rate because Statement II has concrete numbers (₹ 5000). Remember that finding a percentage rate does not always require absolute monetary values if proportional relationships (like doubling) are provided. ### Final Answer Therefore, the correct answer is **if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;**.