Mr. Gupta borrowed a sum of money on compound interest and plans to repay the entire amount at the end of 2 years. Under which of the following sets of statements can the amount to be repaid be uniquely determined? I. The rate of interest is 5% per annum. II. The simple interest earned on the same sum in one year at the same rate is Rs. 600. III. The amount borrowed is 10 times the simple interest earned in 2 years at the same rate.

Introduction / Context:
This is a data sufficiency question based on compound interest. Instead of directly asking you to calculate the final amount, it asks which combination of given statements is enough to determine the amount that Mr. Gupta must repay after 2 years at compound interest.

Given Data / Assumptions:

Mr. Gupta borrows a sum on compound interest for 2 years.
I: The rate of interest is 5% per annum.
II: Simple interest on the same sum in one year at the same rate is Rs. 600.
III: The amount borrowed equals 10 times the simple interest in 2 years at the same rate.
We must decide which statements (alone or in combination) are sufficient to determine the amount payable after 2 years.

Concept / Approach:
We use compound interest and simple interest relations. For principal P and annual rate r%, simple interest for 1 year is P * r / 100 and for 2 years is 2P * r / 100. For compound interest, the amount after 2 years is P * (1 + r/100)^2. A set of statements is sufficient if P and r can be uniquely found, because then the amount is uniquely determined.

Step-by-Step Solution:
From I alone: we know r = 5% but not P, so the amount cannot be found. Not sufficient. From II alone: P * r / 100 = 600 gives one equation with two unknowns P and r. Not sufficient. From III alone: P = 10 * (2P * r / 100) implies 1 = 20r / 100, so r = 5%. Rate is known but P is still unknown. Not sufficient. I + II together: r = 5%, and P * 5 / 100 = 600 gives P = 12,000. Amount after 2 years can now be found, so this pair is sufficient. II + III together: III gives r = 5%. Using II again gives P = 12,000. This pair is also sufficient. I + III together: both only confirm r = 5% but give nothing new about P. Still insufficient.

Verification / Alternative check:
Once P = 12,000 and r = 5% are known from II with either I or III, the amount is P * (1.05)^2 = 12,000 * 1.1025 = Rs. 13,230, which is uniquely determined. No other combination besides II with either I or III allows us to determine both P and r.

Why Other Options Are Wrong:
Only I or only III never give P. Statement II alone leaves both P and r unknown. Even I and III together only fix r. Therefore any option claiming sufficiency without using II in combination is incorrect.

Common Pitfalls:
Many learners treat data sufficiency as if they must always compute the final numeric answer. Here the focus is only on whether the information is enough. Another mistake is not checking all combinations that involve statement II, which is the key to obtaining P once the rate is known.

Final Answer:
The correct choice is Statement II together with either statement I or statement III is sufficient.