Mr Gupta borrows a certain sum of money on compound interest and plans to repay the entire amount at the end of 2 years. In how many of the following statement combinations is the information sufficient to determine the exact amount he has to repay? I. The rate of interest is 5 percent per annum. II. The simple interest on the same sum for 1 year at the same rate is Rs 600. III. The sum borrowed is 10 times the simple interest for 2 years at the same rate.

Introduction / Context:
This is a data sufficiency style question based on compound interest and simple interest. Instead of directly asking for a numerical answer, it asks which set of given statements provides enough information to determine the amount Mr Gupta must repay after 2 years on compound interest. Such questions test both conceptual understanding of interest formulas and logical reasoning about which pieces of data are truly necessary and sufficient for a unique solution.

Given Data / Assumptions:

• Mr Gupta borrows a principal amount P on compound interest.
• The repayment is due at the end of 2 years.
• Statement I: The rate of interest is 5 percent per annum.
• Statement II: Simple interest on the same sum for 1 year at the same rate is Rs 600.
• Statement III: The sum borrowed is 10 times the simple interest for 2 years at the same rate.
• We assume all statements refer to the same principal and the same annual rate of interest.

Concept / Approach:
For compound interest, amount after 2 years is:
A = P * (1 + r / 100)^2To compute A, we must know both P (the principal) and r (the annual rate). The data sufficiency task is to check which combination of statements allows us to uniquely determine both P and r. Simple interest information gives relationships among P, r, and time using:
SI = P * r * T / 100

Step-by-Step Solution:
Step 1: Analyze Statement I alone. It tells us r = 5% per annum, but does not give P. Hence we cannot compute A, so I alone is not sufficient.Step 2: Analyze Statement II alone. It states that SI for 1 year is Rs 600. Using SI = P * r * 1 / 100, we get P * r = 60000. This is only one equation in two unknowns (P and r). Hence II alone is not sufficient.Step 3: Analyze Statement III alone. It says the amount borrowed P is 10 times the simple interest for 2 years. SI for 2 years is P * r * 2 / 100. So P = 10 * (P * r * 2 / 100) which simplifies to 1 = 20r / 100, giving r = 5%. Principal P cancels out and remains unknown, so III alone is not sufficient.Step 4: Combine I and II. From I, r = 5. From II, P * r = 60000, so P * 5 = 60000, giving P = 12000. With both P and r known, A can be determined uniquely. Thus, I and II together are sufficient.Step 5: Combine II and III. From III, we again find r = 5. Using II, P * r = 60000, so P = 12000. Again, we can compute the exact amount A. Therefore II and III together are also sufficient.Step 6: Combine I and III. Both give r = 5%, but do not fix P. Therefore, together they are still insufficient to find A.

Verification / Alternative check:
Once P = 12000 and r = 5 are known (from II plus either I or III), the amount after 2 years of compound interest would be A = 12000 * (1 + 5 / 100)^2 = 12000 * 1.1025 = 13230. This confirms there is a unique answer when those combinations of statements are used. The exact numerical value is not required in the data sufficiency options, but verifying it shows consistency.

Why Other Options Are Wrong:
Statement I alone lacks the principal, so Option A is not correct. Statement III alone also fails to give P, so Option B is not correct. Claiming that either I or II alone is sufficient (Option C) is wrong, because each leaves at least one unknown. Option E, saying all three statements are necessary, is incorrect because we already saw that II with either I or III is enough. Only Option D correctly states that statements II and either I or III together suffice.

Common Pitfalls:
A common error is to think that knowing the rate alone or knowing simple interest alone is enough to find the compound amount, forgetting that both principal and rate are needed. Another mistake is failing to notice that Statement III actually determines the rate by eliminating the principal from the equation. Students may also mistakenly believe that all three statements must be combined, without checking that smaller combinations already provide a complete solution.

Final Answer:
The amount to be repaid after 2 years can be uniquely determined only when we use Statement II together with either Statement I or Statement III, so the correct choice is Statements II and either I or III together are sufficient.