Each of these questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question.
What is the total compound interest earned at the end of three years?
(A) Simple Interest earned on that amount at the same rate and for the same period is Rs. 4500
(B) The rate of interest is 10 pcpa
(C) Compound Interest for three years is more than the simple interest for that period by Rs. 465

Options

A. only A and B
B. Only B and C
C. Only A and C
D. Either A or C and B

Answer

To find the total compound interest earned at the end of three years, we can analyze the given statements step by step.

### Step 1: Understand the Question
We need to calculate the total compound interest earned at the end of three years.

### Step 2: Analyze the Statements
1. **Statement A**: Simple Interest earned on that amount at the same rate and for the same period is Rs. 4500.
2. **Statement B**: The rate of interest is 10% per annum.
3. **Statement C**: Compound Interest for three years is more than the simple interest for that period by Rs. 465.

### Step 3: Use Statement B
From Statement B, we know the rate of interest is 10% per annum. This information is essential to calculate both simple interest and compound interest.

### Step 4: Use Statement A
Using Statement A, we know that the simple interest earned is Rs. 4500. We can use the formula for simple interest:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (10%)
- \( T \) = Time period (3 years)

From this, we can find the principal amount \( P \):
\[ 4500 = \frac{P \times 10 \times 3}{100} \]
\[ 4500 = \frac{30P}{100} \]
\[ 4500 = 0.3P \]
\[ P = \frac{4500}{0.3} = 15000 \]

### Step 5: Calculate Compound Interest Using Statement C
Now we can use Statement C, which states that the compound interest for three years is more than the simple interest by Rs. 465.

Let \( CI \) be the compound interest. According to Statement C:
\[ CI = SI + 465 \]
Substituting the value of \( SI \):
\[ CI = 4500 + 465 = 4965 \]

### Conclusion
The total compound interest earned at the end of three years is Rs. 4965.

### Summary of Necessary Statements
- **Statement B** is necessary to know the rate of interest.
- **Statement A** is necessary to find the principal amount.
- **Statement C** is necessary to find the compound interest based on the difference from simple interest.

### Final Answer
The necessary statements to answer the question are **A, B, and C**.

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