The differnce between C.I and S.I. On a certain sum at the rate of 10% per annum for 2 years is ₹122.Find that sum(in₹)

Options

A. ₹12,000
B. ₹12,400
C. ₹12,200
D. ₹13,400

Explanation

To solve the problem of finding the sum based on the difference between Compound Interest (C.I) and Simple Interest (S.I) over 2 years at a rate of 10%, we can follow these steps:

### Step 1: Understand the Given Information
- The difference between C.I and S.I is given as ₹122.
- The rate of interest (R) is 10% per annum.
- The time period (T) is 2 years.

**Hint:** Identify the key components of the problem: the difference between C.I and S.I, the rate, and the time.

### Step 2: Write the Formula for C.I and S.I
The formula for Simple Interest (S.I) is:
\[ \text{S.I} = \frac{P \times R \times T}{100} \]

The formula for Compound Interest (C.I) is:
\[ \text{C.I} = P \left(1 + \frac{R}{100}\right)^T - P \]

### Step 3: Set Up the Equation
The difference between C.I and S.I can be expressed as:
\[ \text{C.I} - \text{S.I} = 122 \]

Substituting the formulas:
\[ P \left(1 + \frac{R}{100}\right)^T - P - \frac{P \times R \times T}{100} = 122 \]

### Step 4: Substitute the Values
Substituting R = 10 and T = 2 into the equation:
\[ P \left(1 + \frac{10}{100}\right)^2 - P - \frac{P \times 10 \times 2}{100} = 122 \]

This simplifies to:
\[ P \left(1 + 0.1\right)^2 - P - \frac{P \times 20}{100} = 122 \]

### Step 5: Calculate the Compound Interest Term
Calculating \( \left(1 + 0.1\right)^2 \):
\[ \left(1.1\right)^2 = 1.21 \]

Substituting back into the equation:
\[ P \times 1.21 - P - \frac{P \times 20}{100} = 122 \]

### Step 6: Simplify the Equation
This can be simplified to:
\[ P \times 1.21 - P - 0.2P = 122 \]
\[ P \times (1.21 - 1 - 0.2) = 122 \]
\[ P \times 0.01 = 122 \]

### Step 7: Solve for P
Now, we can solve for P:
\[ P = \frac{122}{0.01} \]
\[ P = 12200 \]

### Final Answer
The sum (P) is ₹12200.

---