What is the CI after 3 yr ?
I. Rate is 5 %
II After two years , Difference between Cl and SI is Rs 20.

Options

A. If the statement I alone is sufficient to answer the question but the statement II alone is not sufficient
B. If the statement II alone is sufficient to answer the question but the statement I alone is not sufficient
C. If both statements I and II together are needed to answer the question
D. if either the statement I alone or statment II alone is sufficient to answer the question

Answer

To find the compound interest (CI) after 3 years given the information from the statements, we can follow these steps:

### Step 1: Understand the Given Information
We have two statements:
1. The rate of interest is 5%.
2. After two years, the difference between compound interest (CI) and simple interest (SI) is Rs 20.

### Step 2: Analyze Statement 1
From Statement 1, we know the rate of interest is 5%. However, this information alone is not sufficient to calculate the CI after 3 years because we also need the principal amount.

**Hint:** Remember that knowing only the rate does not provide enough information to calculate CI without the principal.

### Step 3: Analyze Statement 2
From Statement 2, we know that the difference between CI and SI after 2 years is Rs 20. The formula for the difference between CI and SI after 'n' years is given by:

\[ \text{CI} - \text{SI} = P \left( \frac{r}{100} \right)^2 \]

where \( P \) is the principal and \( r \) is the rate of interest.

Given that the difference is Rs 20, we can write:

\[ P \left( \frac{5}{100} \right)^2 = 20 \]

### Step 4: Solve for Principal (P)
Substituting the rate into the equation:

\[ P \left( \frac{1}{20} \right)^2 = 20 \]

This simplifies to:

\[ P \cdot \frac{1}{400} = 20 \]

Multiplying both sides by 400 gives:

\[ P = 20 \times 400 = 8000 \]

### Step 5: Calculate CI for 3 Years
Now that we have the principal (P = Rs 8000), we can calculate the CI for 3 years using the formula for CI:

\[ \text{CI} = P \left(1 + \frac{r}{100}\right)^n - P \]

Substituting the values:

\[ \text{CI} = 8000 \left(1 + \frac{5}{100}\right)^3 - 8000 \]

Calculating \( \left(1 + \frac{5}{100}\right)^3 = (1.05)^3 \):

\[ (1.05)^3 = 1.157625 \]

Now substituting back:

\[ \text{CI} = 8000 \times 1.157625 - 8000 \]

Calculating:

\[ \text{CI} = 9261 - 8000 = 1261 \]

Thus, the compound interest after 3 years is Rs 1261.

### Final Answer
The CI after 3 years is **Rs 1261**.