Data Sufficiency – Simple Interest Rate on a Loan: At what simple interest rate per annum (in %) did Anand pay interest to Deepak? Statement I: Anand borrowed ₹8,000 from Deepak for 4 years. Statement II: Anand returned ₹8,800 to Deepak at the end of 2 years and settled the loan under simple interest.

Introduction / Context:
This is another data sufficiency question involving simple interest. You must decide whether the given statements provide enough information to determine the simple interest rate at which Anand paid interest to Deepak. The focus is on logical sufficiency, not just computation, so you must analyse each statement separately and then together.

Given Data / Assumptions:

• Simple interest is charged at a constant annual rate r%.
• Principal borrowed from Deepak = P.
• Statement I: P = ₹8,000 and the intended loan duration mentioned is 4 years.
• Statement II: Anand repaid ₹8,800 after 2 years and closed the loan.
• Interest is simple, not compound.

Concept / Approach:
Under simple interest, I = (P * r * t) / 100. To find r, we need P, I, and t. Data sufficiency questions ask whether these pieces of information can be uniquely determined. Statement I gives P and a time period but no information about the actual interest paid. Statement II gives a repayment amount and time but does not explicitly state P. Only by combining them do we know both P and the amount repaid after a known time.

Step-by-Step Solution:
Step 1: Consider Statement I alone. It says Anand borrowed ₹8,000 for 4 years. Step 2: Without knowing how much he repaid or what interest was charged, we cannot find the rate r from Statement I alone. Step 3: Therefore, Statement I alone is not sufficient. Step 4: Consider Statement II alone. It tells us that Anand repaid ₹8,800 after 2 years, settling the loan. Step 5: Statement II does not explicitly tell us what the original principal P was; we only know the total repayment and time, not how much of this is principal versus interest. Step 6: Without knowing P, we cannot find r from Statement II alone, since many combinations of P and r could give the same total of ₹8,800 after 2 years. Step 7: Combine Statements I and II. From I, P = ₹8,000. Step 8: From II, total repayment after 2 years is ₹8,800, so interest I over 2 years = 8,800 − 8,000 = ₹800. Step 9: Apply SI formula: I = (P * r * t) / 100 ⇒ 800 = (8,000 * r * 2) / 100. Step 10: Simplify: 800 = 160r, so r = 800 / 160 = 5% per annum.

Verification / Alternative check:
Check with r = 5% per annum, P = ₹8,000, and t = 2 years. SI = (8,000 * 5 * 2) / 100 = 800. Amount = 8,000 + 800 = ₹8,800, which matches Statement II. The 4 year mention in Statement I is not used directly in the calculation but still appears as part of the loan description; what matters is that both statements are needed to fix P and I over a specific period.

Why Other Options Are Wrong:

• Statement I alone is sufficient: Incorrect, because interest or repayment is not provided.
• Statement II alone is sufficient: Incorrect, because original principal is not given.
• Either statement alone is sufficient: Incorrect, since neither alone is enough.
• Both statements not sufficient: Incorrect, as combining them allows us to calculate r uniquely.

Common Pitfalls:
Some students incorrectly assume Statement II implies that ₹8,800 is entirely interest or misread the time periods. Others ignore the need to know both principal and interest to find the rate. In data sufficiency, always identify how many independent equations you have and whether they are enough to determine the required variable uniquely.

Final Answer:
The correct choice is Both Statement I and Statement II are necessary to determine the rate of interest.