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., 2006) I. Simple interest earned per annum is ₹ 5300. II. The difference between the compound and simple interest on an amount is ₹ 1060 at the end of 2 years. III. An amount doubles itself in 5 years with simple interest.

### Concept & Evaluating Multiple Statements When given three statements in Data Sufficiency, test each independently first, then in pairs. The goal is to find the minimum information required to find the rate of interest ($R$). ### Step-by-Step Solution 1. **Evaluate III alone:** An amount doubles in 5 years at simple interest. This means $SI = P$. Formula: $P = \frac{P \times R \times 5}{100} \Rightarrow R = 20\%$. Statement III alone is sufficient. 2. **Evaluate I and II together:** Statement I: $SI$ per annum = ₹ 5300. Thus, $\frac{P \times R}{100} = 5300$. Statement II: $CI - SI$ for 2 yrs = ₹ 1060. Thus, $P(\frac{R}{100})^2 = 1060$. Divide II by I: $\frac{P(\frac{R}{100})^2}{\frac{P \times R}{100}} = \frac{1060}{5300} \Rightarrow \frac{R}{100} = 0.2 \Rightarrow R = 20\%$. Statements I and II together are also sufficient. 3. **Conclusion:** The rate can be found using either III alone, or I and II together. ### Exam Strategy & Shortcut Always check the simplest statement first. Statement III is a classic standard property (doubling in 5 years always means $R = \frac{100}{5} = 20\%$). Finding this immediately narrows down the options. ### Common Pitfall Stopping after finding one sufficient statement (like III) and choosing "Only III" without checking if combinations of the remaining statements also work. ### Final Answer Therefore, the correct answer is **Only III or I and II**.