Interest earned on a certain sum in 2 years at 20% pa at CI is twice the interest earned on Rs. 1100 for 2 yrs at 10% Sl. Find sum.

Options

A. A)Rs. 1000
B. B)Rs.500
C. C)Rs.750
D. D)Rs.1250

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Simple Interest (SI) on Rs. 1100 for 2 years at 10% per annum.
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \(P = 1100\) (Principal)
- \(R = 10\%\) (Rate of interest)
- \(T = 2\) (Time in years)

Substituting the values:
\[ \text{SI} = \frac{1100 \times 10 \times 2}{100} = \frac{22000}{100} = 220 \]

### Step 2: Determine the Compound Interest (CI) for the unknown principal at 20% per annum for 2 years.
Let the unknown principal be \(P\). The formula for Compound Interest is:
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \(R = 20\%\)
- \(T = 2\)

Substituting the values:
\[ \text{CI} = P \left(1 + \frac{20}{100}\right)^2 - P = P \left(1.2^2\right) - P = P \left(1.44\right) - P = 0.44P \]

### Step 3: Set up the equation based on the problem statement.
According to the problem, the CI earned on the unknown principal is twice the SI calculated in Step 1:
\[ 0.44P = 2 \times 220 \]
\[ 0.44P = 440 \]

### Step 4: Solve for the unknown principal \(P\).
To find \(P\):
\[ P = \frac{440}{0.44} = 1000 \]

### Conclusion
The sum (principal amount) is Rs. 1000.