What is the rate of interest per cent per annum? Data I: An amount doubles itself in 5 years on simple interest. Data II: The difference between compound interest and simple interest on a certain amount in 2 years is Rs. 400. Data III: The simple interest earned per annum is Rs. 2000.

Introduction / Context:
This is a data sufficiency question based on simple and compound interest. We are not asked to find the numerical value of the rate of interest itself, but to decide which group of statements provides enough information to determine the rate per cent per annum in a unique way.

Given Data / Assumptions:

• Statement I: An amount doubles in 5 years on simple interest.
• Statement II: The difference between compound interest and simple interest on a certain amount in 2 years is Rs. 400.
• Statement III: The simple interest earned per year on the same amount is Rs. 2000.
• We assume the same principal and the same rate of interest throughout a set of statements.

Concept / Approach:

For simple interest, SI = P * r * t / 100. For compound interest over 2 years, CI = P * [(1 + r/100)^2 - 1]. The difference CI - SI for 2 years equals P * r^2 / 100^2. We check each statement or combination to see if the rate r becomes uniquely determined.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Statement I only is already sufficient, but option A ignores that II and III together are also sufficient. Option B ignores that Statement I alone is enough. Option C claims all three are required, which is incorrect, since we can find the rate from I alone or from II and III together. Only option D correctly states that either Statement I alone or the combination of Statements II and III alone is sufficient.

Common Pitfalls:

Students sometimes try to compute the exact rate numerically for data sufficiency questions, which is not necessary. Another common error is to treat each statement in isolation and forget that certain pairs of statements can together determine all unknowns. Understanding the structure of the formulas for simple and compound interest is essential to judge sufficiency correctly.

Final Answer:

The rate of interest can be found either from Statement I alone or from Statements II and III together, so the correct choice is Statement I only or Statements II and III only.