An amount of money was lent for 3 years at a certain rate of interest. What will be the difference between the simple interest and the compound interest earned on it at the same rate and for the same period? I. The rate of interest was 8% per annum. II. The total simple interest earned in 3 years was Rs 1,200. Based on these statements, is the information sufficient to determine that difference?

Introduction:
This question is a data sufficiency problem related to the difference between simple and compound interest over 3 years. Instead of computing the numeric answer directly, you must decide whether the given statements provide enough information to determine that difference uniquely.

Given Data / Assumptions:

• We have some unknown principal P lent for 3 years.
• We want the difference between CI and SI after 3 years at the same rate.
• Statement I: Rate of interest r = 8% per annum.
• Statement II: Total simple interest for 3 years = Rs 1,200.

Concept / Approach:
For time t = 3 years and rate r, simple interest is:
SI = P * r * t / 100Compound interest over 3 years is related to P and r by:
CI = P * ((1 + r/100)^3 - 1)The difference between CI and SI is a function of both P and r. To determine this difference, we must know both P and r. Therefore, we will analyze whether the statements together or individually give us both these values.

Step-by-Step Analysis of Statements:
Step 1: Statement I alone.Statement I gives only r = 8% per annum.Principal P is unknown, so we cannot compute SI or CI numerically, hence the difference cannot be found.Statement I alone is not sufficient.Step 2: Statement II alone.Statement II gives SI = Rs 1,200 for 3 years.We know the product P * r but not their individual values, because:1,200 = P * r * 3 / 100So P * r is fixed, but P and r individually are not determined.Statement II alone is not sufficient.Step 3: Combine Statements I and II.From I: r = 8%From II: 1,200 = P * 8 * 3 / 1001,200 = P * 24 / 1001,200 = 0.24 * PSo P = 1,200 / 0.24 = Rs 5,000Now both P and r are known.With P and r known, we can compute SI and CI for 3 years and hence their difference. Therefore, both statements together are sufficient to answer the question.

Verification / Alternative check:
With P = Rs 5,000 and r = 8%, SI for 3 years is already given as Rs 1,200. CI can be computed using:
CI = 5,000 * ((1.08)^3 - 1)The difference CI - SI would be a single definite number, showing that the data is sufficient.

Why Other Options Are Wrong:

• Option a and b: Each statement alone clearly lacks either P or r.
• Option c and e: They claim that even together the statements are not sufficient, which is incorrect because together they uniquely determine both P and r.

Common Pitfalls:
Students sometimes think that knowing SI for 3 years is enough to compute CI, forgetting that the rate must also be known. In data sufficiency questions, always identify how many unknowns exist and whether the combined information gives you enough independent equations to solve for those unknowns exactly.

Final Answer:
Both statements I and II together are necessary and sufficient to determine the required difference between simple interest and compound interest.