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 will be the compound interest after 3 years? I. Rate of interest is 5 percent. II. The difference between the total simple interest and the total compound interest after 2 years is ₹ 20.

### Concept & Difference Formula To calculate compound interest for any period, you require the Principal ($P$) and the Rate ($R$). The difference between Compound Interest and Simple Interest for a 2-year period provides an equation relating $P$ and $R$. $$\text{Difference} = P\left(\frac{R}{100}\right)^2$$ ### Step-by-Step Solution From Statement I: * Given: $R = 5\%$. Principal is unknown. Not sufficient. From Statement II: * Given: $C.I. - S.I.$ for 2 years = 20. Both $P$ and $R$ are unknown. Not sufficient. Combining Statement I and II: * We have $R = 5\%$ and the 2-year difference = 20. * Using the formula: $20 = P\left(\frac{5}{100}\right)^2$ * $20 = P\left(\frac{25}{10000}\right) \Rightarrow P = \frac{20 \times 10000}{25} = 8000$. * Now we have $P = 8000$, $R = 5\%$, and $T = 3$ years. We can fully calculate the Compound Interest. * Therefore, both statements together are necessary. ### Exam Strategy & Shortcut Whenever a question asks for a final financial value (like CI or Amount) and only gives you a rate in one statement and a flat monetary difference in another, you will almost always need both statements to find the base Principal before solving the main question. ### Common Pitfall Attempting to solve the difference equation from Statement II without realizing that there are two unknown variables ($P$ and $R$), making it unsolvable on its own. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**