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 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 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 percentage of simple interest per annum did Anand pay to Deepak ? I. Anand borrowed ₹ 8000 from Deepak for four years. II. Anand returned ₹ 8800 to Deepak at the end of two years and settled the loan.

### Concept & Simple Interest Rate To calculate the simple interest rate per annum, we need the Principal ($P$), Total Interest ($SI$), and the actual Time ($T$) the money was held before settlement. $$R = \frac{SI \times 100}{P \times T}$$ ### Step-by-Step Solution * **From the Question:** We need to find the rate of interest ($R$). * **Analyze Statement I:** Anand borrowed $P = ₹ 8000$. The intended duration was $4$ years. However, this statement gives no information about the interest paid or the final amount. It is insufficient alone. * **Analyze Statement II:** Anand returned a total amount $A = ₹ 8800$ to settle the loan at the end of $T = 2$ years. This gives us the total Amount and the actual time, but we don't know the initial Principal borrowed. It is insufficient alone. * **Combine Statements I & II:** * From I, we know the Principal $P = ₹ 8000$. * From II, we know the final Amount $A = ₹ 8800$ and the actual time $T = 2$ years. * We can find the simple interest: $SI = A - P = 8800 - 8000 = ₹ 800$. * Now we have all variables to find the rate: $R = \frac{800 \times 100}{8000 \times 2} = 5\%$. * We needed the data from both statements to reach the answer. ### Exam Strategy & Shortcut Pay close attention to "intended time" versus "actual time." Statement I says he borrowed it "for four years" (intended), but Statement II says he "settled the loan" at the end of two years. You must use the actual settlement time ($T=2$) to calculate the interest rate applied to the money while he held it. ### Common Pitfall A common mistake is discarding both statements because Statement I says 4 years and Statement II says 2 years, assuming contradictory information. In real-life lending (and math problems modeling it), loans can be settled early. The settlement timeframe supersedes the initial term. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question;**.