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 compound interest earned by Robert at the end of 2 years? I. Simple interest at the same rate for one year is ₹ 1020 and the rate of interest is 12 p.c.p.a. II. The amount invested is ₹ 8500.

### Concept & Logic To calculate Compound Interest for 2 years, we need the Principal ($P$) and the Rate ($R$). $$C.I. = P\left[\left(1 + \frac{R}{100}\right)^2 - 1\right]$$ ### Step-by-Step Solution * From Statement I: We are given $S.I. = 1020$ for $T = 1$ year at $R = 12\%$. Using the formula $S.I. = \frac{P \times R \times T}{100}$, we get $1020 = \frac{P \times 12 \times 1}{100}$, which yields $P = 8500$. Now we have $P = 8500$ and $R = 12\%$ to calculate $C.I.$ for 2 years. Sufficient alone. * From Statement II: We are given $P = 8500$. However, the rate $R$ is completely unknown and not provided in the main question body. Not sufficient alone. * Thus, only Statement I is sufficient. ### Exam Strategy & Shortcut Statement I implicitly provides the Principal by giving the Simple Interest for one year along with the rate. Once you spot that a statement provides both $P$ and $R$ (either directly or via a simple 1-step calculation), it is sufficient to solve any standard compound interest query. ### Common Pitfall Assuming Statement II is necessary to confirm the Principal calculated in Statement I. In Data Sufficiency, if Statement I yields a definitive value on its own, it is sufficient, regardless of what Statement II confirms or adds. ### 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;**.