In each of the following questions you have to find out which of the following statements is/are sufficient to answer the given questions. Give appropriate answers according to the options.
A person borrowed a certain sum of money at compound interest for 2 years. What will be the amount required to be returned after 2 years?
1. If the amount was borrowed at simple interest, then, after 5 years ₹600 was required to be paid as simple interest.
II. The rate of interest is `6%` per annum.
III. The sum of money borrowed is 10 times the amount required to be paid as simple interest after 2 years.

Options

A. II and I or III
B. II and III together
C. I and II together
D. All statements are not sufficient to answer the question

Answer

To solve the problem, we need to determine which of the given statements are sufficient to find the amount required to be returned after 2 years for a loan taken at compound interest.

### Step-by-Step Solution:

1. **Understanding the Question**:
We need to find the total amount to be returned after 2 years when a certain sum of money is borrowed at compound interest.

2. **Analyzing Statement I**:
- The statement says that if the amount was borrowed at simple interest, then after 5 years, ₹600 was required to be paid as simple interest.
- From this, we can calculate the simple interest per year:
\[ \text{Simple Interest per year} = \frac{600}{5} = ₹120 \]

3. **Calculating Principal from Statement I**:
- The simple interest formula is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
- Here, we know SI for 5 years is ₹600, but we need to find the principal (P). We will need the rate of interest to find P.

4. **Analyzing Statement II**:
- This statement provides the rate of interest, which is 6% per annum.
- Now, we can use this rate to find the principal:
\[ 600 = \frac{P \times 6 \times 5}{100} \]
- Rearranging gives:
\[ P = \frac{600 \times 100}{6 \times 5} = ₹2000 \]

5. **Calculating Amount After 2 Years**:
- Now that we have the principal (P = ₹2000) and the rate (R = 6%), we can calculate the amount after 2 years using the compound interest formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
- Substituting the values:
\[ A = 2000 \left(1 + \frac{6}{100}\right)^2 = 2000 \left(1.06\right)^2 \]
- Calculating \( (1.06)^2 \):
\[ (1.06)^2 = 1.1236 \]
- Therefore:
\[ A = 2000 \times 1.1236 = ₹2247.20 \]

6. **Analyzing Statement III**:
- This statement says that the sum of money borrowed is 10 times the amount required to be paid as simple interest after 2 years.
- Let the simple interest for 2 years be \( X \). Then, the principal \( P = 10X \).
- The simple interest for 2 years can be calculated as:
\[ X = \frac{P \times R \times 2}{100} \]
- Substituting \( P = 10X \):
\[ X = \frac{10X \times R \times 2}{100} \]
- This leads to:
\[ 100X = 20X \times R \implies R = \frac{100}{20} = 5\% \]
- However, we already know the rate is 6%, so this statement does not provide sufficient information to determine the amount.

### Conclusion:
- The first and second statements together are sufficient to find the amount required to be returned after 2 years.
- The third statement alone is not sufficient.

### Final Answer:
The correct option is that statements I and II together are sufficient to answer the question.