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 simple interest per annum? (R.B.I., 2004) I. An amount of ₹ 7500 increases by ₹ 1125 at the end of one year. II. The principal amount of ₹ 6000 increases by three times in 20 years. III. Interest accrued on an amount of ₹ 5200 in 3 years is ₹ 2340.

### Concept & Determining Rate of Interest To determine the simple rate of interest ($R$), we must have a complete set of values for the Principal ($P$), the Simple Interest ($SI$), and the Time ($T$) so we can isolate $R$ in the formula: $$R = \frac{SI \times 100}{P \times T}$$ ### Step-by-Step Solution * **From the Question:** We are tasked with finding the rate of interest ($R$). Let's evaluate each statement independently. * **Analyze Statement I:** A principal of $P = 7500$ increases by an interest of $SI = 1125$ in $T = 1$ year. * All necessary variables are provided. $R = \frac{1125 \times 100}{7500 \times 1} = 15\%$. (Statement I is sufficient). * **Analyze Statement II:** A principal of $P = 6000$ increases by three times its value, meaning the interest generated is $SI = 3 \times 6000 = 18000$ in $T = 20$ years. * All necessary variables are provided. $R = \frac{18000 \times 100}{6000 \times 20} = \frac{300}{20} = 15\%$. (Statement II is sufficient). * **Analyze Statement III:** A principal of $P = 5200$ accrues an interest of $SI = 2340$ in $T = 3$ years. * All necessary variables are provided. $R = \frac{2340 \times 100}{5200 \times 3} = 15\%$. (Statement III is sufficient). * Because each statement provides a complete set of variables that successfully isolates and solves for the interest rate independently, any single statement works. ### Exam Strategy & Shortcut Scan each statement for the trio of required elements: Principal, Interest (or final Amount), and Time. Statement I gives all three explicitly. Statement II gives all three explicitly. Statement III gives all three explicitly. Thus, each one independently works. No math is required once you verify the variables are present. ### Common Pitfall The phrase "increases by three times" in Statement II can be tricky. It means the *addition* to the principal is $3P$, making the final amount $4P$. Even if misread as "becomes three times" (amount = $3P$, $SI = 2P$), it still provides a clear mathematical path to the rate, so its data sufficiency status remains unaffected. ### Final Answer Therefore, the correct answer is **Any one of the three**.