The following questions are accompanied by three statements A, B and C. You have to determine which statement(s) is/are necessary/sufficient to answer the question.
What is the rate of interest per annum?
A. Difference between compound interest and simple interest for 2 years on the same amount at same rate of interest is Rs.60.
B. Simple interest for five years on the same amount at the same rate is one-fourth of the principal amount.
C. Compound interest for three years on Rs.16000 at the same rate is Rs.2522.

Options

A. Only B alone
B. Only C alone
C. Only A alone
D. Any one of the three alone

Answer

To determine the rate of interest per annum, we will analyze each statement provided and see if they are sufficient to answer the question.

### Step 1: Analyze Statement A
**Statement A:** The difference between compound interest (CI) and simple interest (SI) for 2 years on the same amount at the same rate of interest is Rs. 60.

The formula for the difference between compound interest and simple interest for 2 years is given by:
\[ \text{Difference} = \text{CI} - \text{SI} = P \times \left( \frac{r^2}{100^2} \right) \]
Where:
- \( P \) is the principal amount,
- \( r \) is the rate of interest per annum.

From Statement A, we know:
\[ P \times \left( \frac{r^2}{100^2} \right) = 60 \]

This equation can help us find the rate of interest \( r \) if we know \( P \). However, without knowing \( P \), we cannot determine \( r \) solely from this statement.

**Conclusion:** Statement A alone is not sufficient.

### Step 2: Analyze Statement B
**Statement B:** Simple interest for five years on the same amount at the same rate is one-fourth of the principal amount.

The formula for simple interest is:
\[ \text{SI} = \frac{P \times r \times t}{100} \]
Where \( t = 5 \) years.

From Statement B:
\[ \frac{P \times r \times 5}{100} = \frac{P}{4} \]

By simplifying, we can cancel \( P \) (assuming \( P \neq 0 \)):
\[ \frac{r \times 5}{100} = \frac{1}{4} \]

This gives:
\[ r = \frac{100}{5} \times \frac{1}{4} = 5 \]

Thus, we can find the rate of interest \( r \) from Statement B alone.

**Conclusion:** Statement B alone is sufficient.

### Step 3: Analyze Statement C
**Statement C:** Compound interest for three years on Rs. 16,000 at the same rate is Rs. 2522.

The formula for compound interest is:
\[ \text{CI} = P \left(1 + \frac{r}{100}\right)^t - P \]
Where:
- \( P = 16000 \),
- \( t = 3 \).

From Statement C, we have:
\[ 2522 = 16000 \left(1 + \frac{r}{100}\right)^3 - 16000 \]

Rearranging gives:
\[ 16000 \left(1 + \frac{r}{100}\right)^3 = 16000 + 2522 \]
\[ \left(1 + \frac{r}{100}\right)^3 = \frac{18522}{16000} \]

Taking the cube root will allow us to solve for \( r \). Thus, we can find the rate of interest \( r \) from Statement C alone.

**Conclusion:** Statement C alone is sufficient.

### Final Conclusion
- Statement A is not sufficient.
- Statement B is sufficient.
- Statement C is sufficient.

Therefore, the answer is that either Statement B or Statement C alone is sufficient to determine the rate of interest per annum.