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 simple interest 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 compound interest case. Compare the two principals and choose the correct relationship between Quantity I and Quantity II.

Introduction / Context:
This is a comparison based aptitude question where the candidate must compute two separate principal amounts using different interest models and then compare the results. Quantity I uses simple interest over 3 years, while Quantity II uses compound interest over 2 years. Such problems are common in banking and insurance exams, where candidates must quickly evaluate which of the two quantities is greater without necessarily focusing on the absolute amounts beyond what is needed for comparison.

Given Data / Assumptions:

• Quantity I: Simple interest SI1 = Rs 4800.
• Simple interest rate for Quantity I, R1 = 5% per annum.
• Time for Quantity I, T1 = 3 years.
• Quantity II: Compound interest CI2 = Rs 3708.
• Compound interest rate for Quantity II, R2 = 6% per annum.
• Time for Quantity II, T2 = 2 years with annual compounding.
• Principals in the two cases may be different and must be found separately.

Concept / Approach:
For Quantity I with simple interest, the formula is:
SI1 = (P1 * R1 * T1) / 100 We can rearrange this to find P1. For Quantity II with compound interest, we use:
Amount A2 = P2 * (1 + R2 / 100) ^ T2 Compound interest CI2 = A2 − P2 By expressing CI2 in terms of P2 and equating to Rs 3708, we can solve for P2. Once P1 and P2 are obtained, they are compared to determine the correct option.

Step-by-Step Solution:
For Quantity I (simple interest): SI1 = Rs 4800, R1 = 5% per annum, T1 = 3 years. 4800 = (P1 * 5 * 3) / 100. 4800 = (15P1) / 100. 4800 = 0.15P1. P1 = 4800 / 0.15 = 32000. So, Quantity I principal = Rs 32000. For Quantity II (compound interest): CI2 = Rs 3708, R2 = 6% per annum, T2 = 2 years. Let the principal be P2. Amount A2 = P2 * (1 + 6 / 100) ^ 2 = P2 * (1.06) ^ 2. (1.06) ^ 2 = 1.1236, so A2 = 1.1236P2. Compound interest CI2 = A2 − P2 = 1.1236P2 − P2 = 0.1236P2. Given CI2 = 3708, so 0.1236P2 = 3708. P2 = 3708 / 0.1236 = 30000. Thus Quantity II principal = Rs 30000.

Verification / Alternative check:
We can quickly recheck both values. For Quantity I, 5% of 32000 is 1600 per year, and for 3 years the interest is 1600 * 3 = 4800, which matches. For Quantity II, 6% of 30000 is 1800 for the first year, so amount becomes 31800. Six percent of 31800 is 1908 for the second year, making the total amount 33708. Compound interest is 33708 − 30000 = 3708, which agrees with the given data. Thus both principal values are correct.

Why Other Options Are Wrong:
Since P1 = 32000 and P2 = 30000, clearly Quantity I is greater than Quantity II. Therefore, options suggesting equality or the reverse inequality, such as Quantity I ≤ Quantity II, Quantity I < Quantity II, or Quantity I = Quantity II, are incorrect. Quantity I ≥ Quantity II is technically correct but less precise than the strict inequality, so the best answer is Quantity I > Quantity II.

Common Pitfalls:
Some students may miscalculate (1.06) ^ 2 or may take compound interest simply as 2 times 6% of the principal, which would be wrong. Others might mix up the interest and amount or forget to subtract the principal when calculating compound interest. Careful arithmetic and a clear distinction between amount and interest are essential. Also, one must remember that the simplest correct comparison is Quantity I > Quantity II, not just a weak inequality.

Final Answer:
Since the principal in Quantity I is Rs 32000 and the principal in Quantity II is Rs 30000, the correct relationship is Quantity I > Quantity II.