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 given 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 even 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. 2004) I. Difference between compound interest and the simple interest accrued on an amount of ₹ 15000 in 3 years is ₹ 673.92. II. In 2 years, an amount of ₹ 6500 fetches simple interest of ₹ 1560.

### Concept & Logic To determine the rate of interest ($R$), we need to see if each statement can independently provide a solvable equation for $R$. ### Step-by-Step Solution From Statement I: * The difference between CI and SI for 3 years is given by: $$P(R/100)^2 (3 + R/100) = \text{Difference}$$ * We are given $P = 15000$ and Difference $= 673.92$. * This gives us a cubic equation in terms of $R$. Since all constants are positive, there is a unique positive real solution for $R$. Thus, Statement I alone is sufficient. From Statement II: * SI for 2 years on ₹ 6500 is ₹ 1560. * Using the formula $SI = (P \times R \times T) / 100$: $$1560 = \frac{6500 \times R \times 2}{100}$$ * This is a linear equation with only one variable, $R$. Statement II alone is sufficient. ### Exam Strategy & Shortcut Recognize standard formulas immediately. Statement I provides all variables for the 3-year CI-SI difference formula except $R$. Statement II provides all variables for the basic SI formula except $R$. Both are individually sufficient. ### Common Pitfall Students often skip Statement I, assuming a 3-year difference formula is too complex to guarantee a unique solution, but for positive financial values, it does yield a unique real rate. ### Final Answer Therefore, the correct answer is **if the data either in Statement I or in Statement II alone are sufficient to answer the question;**