If the compound interest on a certain sum for 2 years at `12.5%` per annum is Rs.170, the simple interest is-

Options

A. Rs.150
B. Rs.152.50
C. Rs.160
D. Rs.162.50

Answer

To solve the problem step by step, we will first find the principal amount using the given compound interest, and then we will calculate the simple interest.

### Step 1: Understand the given information
We are given:
- Compound Interest (CI) for 2 years = Rs. 170
- Rate of interest (R) = 12.5% per annum
- Time (T) = 2 years

### Step 2: Use the formula for Compound Interest
The formula for Compound Interest is:
\[ CI = A - P \]
where \( A \) is the amount after time \( T \) and \( P \) is the principal.

The formula for the amount \( A \) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ 170 = P \left(1 + \frac{12.5}{100}\right)^2 - P \]
This simplifies to:
\[ 170 = P \left(1.125\right)^2 - P \]

### Step 4: Calculate \( (1.125)^2 \)
Calculating \( (1.125)^2 \):
\[ (1.125)^2 = 1.265625 \]
So, we can rewrite the equation as:
\[ 170 = P(1.265625 - 1) \]
\[ 170 = P(0.265625) \]

### Step 5: Solve for \( P \)
Now, we can solve for \( P \):
\[ P = \frac{170}{0.265625} \]
Calculating this gives:
\[ P \approx 640 \]

### Step 6: Calculate Simple Interest (SI)
Now that we have the principal \( P \), we can calculate the Simple Interest using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{640 \times 12.5 \times 2}{100} \]
Calculating this gives:
\[ SI = \frac{64000}{100} = 640 \]

### Final Answer
The simple interest is Rs. 160.

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