Each question contains Quantity I and Quantity II. Read carefully and compare the two values. Quantity I: The simple interest on a certain sum of money for 3 years at 5% per annum is Rs. 4800, so find the principal in this case. Quantity II: The compound interest on a certain sum of money for 2 years at 6% per annum is Rs. 3708, so find the principal in this case. Compare the two principals and choose the correct relationship.

Introduction / Context:
Quantity comparison questions are popular in competitive exams because they test both conceptual understanding and speed. Here, two different principals are hidden inside two statements, one involving simple interest and the other involving compound interest. The learner must compute each principal separately and then determine whether Quantity I is greater than, less than, or equal to Quantity II. Mastery of both simple and compound interest formulas is essential to solve this question confidently.

Given Data / Assumptions:
Quantity I: Simple interest amount is Rs. 4800 at 5 percent per annum for 3 years.
Quantity II: Compound interest amount is Rs. 3708 at 6 percent per annum for 2 years.
Interest for Quantity I is simple interest, not compound interest.
Interest for Quantity II is compound interest with annual compounding.
We must find principal P1 for Quantity I and principal P2 for Quantity II and then compare P1 and P2.

Concept / Approach:
For Quantity I, simple interest I is given by I = P1 * r * t / 100. Since I, r, and t are known, we can directly solve for P1. For Quantity II, we use the compound interest relationship A = P2 * (1 + r / 100)^n, where A is amount and CI = A - P2. The problem gives CI, so we set P2 * [(1 + r / 100)^n - 1] equal to 3708 and solve for P2. After obtaining both principals, we compare them numerically to decide which quantity is larger.

Step-by-Step Solution:
For Quantity I, let the principal be P1 rupees.Simple interest I1 = 4800, rate r1 = 5 percent, time t1 = 3 years.Use I1 = P1 * r1 * t1 / 100 to get 4800 = P1 * 5 * 3 / 100.Simplify 5 * 3 / 100 = 15 / 100 = 0.15, so 4800 = 0.15P1.Thus P1 = 4800 / 0.15 = 32000 rupees.For Quantity II, let the principal be P2 rupees.Rate r2 = 6 percent per annum, time t2 = 2 years, compound interest CI2 = 3708.Amount factor for 2 years is (1 + 6 / 100)^2 = (1.06)^2 = 1.1236.Compound interest CI2 = P2 * (1.1236 - 1) = P2 * 0.1236.So 3708 = 0.1236P2, which gives P2 = 3708 / 0.1236 = 30000 rupees.Therefore P1 = 32000 and P2 = 30000, so Quantity I is greater than Quantity II.

Verification / Alternative check:
Check Quantity I by computing interest on 32000 at 5 percent for 3 years. Simple interest equals 32000 * 5 * 3 / 100 = 32000 * 15 / 100 = 4800 rupees, which matches the given information. For Quantity II, interest on 30000 at 6 percent per annum compounded for 2 years is 30000 * (1.1236 - 1) = 30000 * 0.1236 = 3708 rupees, which also matches the given data. The principals are correctly determined, and 32000 is clearly larger than 30000.

Why Other Options Are Wrong:
The statement Quantity I ≥ Quantity II is technically true numerically, but in comparison style questions the more precise statement is that Quantity I is strictly greater, so the option with only greater than is preferred here.
The options Quantity I < Quantity II and Quantity I ≤ Quantity II are incorrect because 32000 is not less than 30000.
The option Quantity I = Quantity II is wrong since the two principals are clearly different values.

Common Pitfalls:
Students may forget that 3708 is compound interest, not amount, and accidentally treat it as the final amount A. Another error is miscomputing (1.06)^2, which must be 1.1236. For Quantity I, missing the factor of 3 years in the formula also leads to wrong values. It is important to carefully distinguish between interest and amount, and between principal for each quantity, to avoid such mistakes.

Final Answer:
The principal for Quantity I is greater than the principal for Quantity II, so Quantity I > Quantity II.