For the following data sufficiency question on compound interest, determine which statements give enough information to find the compound amount: I. Rs. 200 was borrowed for 192 months at 6% per annum compounded annually. II. Rs. 200 was borrowed for 16 years at 6% per annum.

Introduction / Context:
This is a data sufficiency question rather than a direct numerical calculation. The focus is on deciding which given statements provide enough information to determine the compound amount. Such questions are designed to test logical reasoning about the information provided rather than detailed arithmetic skills. The key idea is to analyse whether each statement alone, or both together, allow the compound interest formula to be applied without ambiguity.

Given Data / Assumptions:

• We want to determine the compound amount on a borrowed sum.
• Statement I: Rs. 200 was borrowed for 192 months at 6% per annum compounded annually.
• Statement II: Rs. 200 was borrowed for 16 years at 6% per annum.
• We need to see which statements are sufficient to compute the compound amount.
• We assume standard compound interest with annual compounding unless specified otherwise.

Concept / Approach:
To calculate a compound amount using the formula A = P * (1 + r) ^ n, we need the principal P, the annual rate r in decimal form, and the number of years n. Data sufficiency problems ask whether we can identify these quantities uniquely from the given statements. Statement I explicitly provides all three with no ambiguity. Statement II provides the principal, a rate per annum, and a time stated in years, but does not explicitly confirm that the interest is compounded annually, which creates uncertainty about the compounding pattern and thus about the exact compound amount.

Step-by-Step Solution:
Step 1: Examine Statement I. It tells us that P = 200, the duration is 192 months, and the rate is 6% per annum compounded annually. Step 2: Convert the duration in Statement I into years: 192 months equals 192 / 12 = 16 years. Step 3: With Statement I alone, we know P, r = 6% per annum, and n = 16 years, and we also know the compounding frequency is annual. Therefore, we can compute A = 200 * (1.06) ^ 16. Step 4: Now examine Statement II. It says P = 200, time = 16 years at 6% per annum, but it does not explicitly mention that interest is compounded annually. Step 5: Because the compounding frequency is not stated in Statement II, we do not know whether interest is compounded annually, semiannually, quarterly, or in some other way, so the exact compound amount remains uncertain. Step 6: Therefore, Statement II alone is not sufficient to determine the unique compound amount, while Statement I alone is sufficient.

Verification / Alternative check:
If we attempted to treat Statement II as implying annual compounding by assumption, we could compute an amount, but this would rely on an extra assumption not clearly given in the statement. In data sufficiency questions, we must work only with what is explicitly stated. In contrast, Statement I clearly states that the interest is compounded annually, and the total time in months can be converted to years, so there is no ambiguity. Therefore, we confirm that the correct logical conclusion is that only Statement I alone is sufficient.

Why Other Options Are Wrong:
Option B claims that II alone is sufficient while I alone is not, which contradicts the clear information about compounding in Statement I. Option C states that either statement alone is sufficient, which wrongly treats Statement II as fully specifying the compounding structure. Option D says that both statements together are not sufficient, but this is incorrect because Statement I by itself already provides enough information. Option E suggests that both together are required, but, again, Statement I alone is already complete, so the additional Statement II is not necessary for computation.

Common Pitfalls:
Many students casually assume that if a rate is given per annum, then the compounding is automatically annual, which is not always guaranteed. In data sufficiency, such assumptions can lead to incorrect conclusions. Another pitfall is to get distracted by the conversion of months to years and to overlook the important phrase "compounded annually" in Statement I. It is crucial to focus on what is explicitly given and to ask whether the principal, rate, time, and compounding pattern are all clearly determined.

Final Answer:
Only Statement I by itself provides complete information to compute the compound amount, while Statement II alone does not. Therefore, the correct choice is I alone is sufficient while II alone is not sufficient to answer, which is option A.