An equal amount of sum is invested in two schemes for 4 years each, both offering simple interest.. When invested in scheme A at `8%` per annum the sum amounts to Rs 5280. In scheme B, invested at `12%` per annum it amounts to Rs 5920. What is the sum invested ?

Options

A. Rs 4,000
B. Rs 3,500
C. Rs 4' 200
D. Rs 3,200

Answer

To find the sum invested in two schemes, we can follow these steps:

### Step 1: Define the variables
Let the sum invested in each scheme be denoted as \( X \).

### Step 2: Calculate the total amount for Scheme A
For Scheme A, the interest rate is \( 8\% \) per annum, and the investment period is \( 4 \) years. The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (which is \( X \))
- \( R \) = Rate of interest (which is \( 8\% \))
- \( T \) = Time period (which is \( 4 \) years)

The interest earned from Scheme A can be calculated as:
\[ \text{Interest from A} = \frac{X \times 8 \times 4}{100} = \frac{32X}{100} = 0.32X \]

The total amount after 4 years in Scheme A is:
\[ \text{Total Amount in A} = X + \text{Interest from A} = X + 0.32X = 1.32X \]
According to the problem, this total amount equals Rs 5280:
\[ 1.32X = 5280 \]

### Step 3: Solve for \( X \) from Scheme A
To find \( X \), we can rearrange the equation:
\[ X = \frac{5280}{1.32} \]

Calculating this gives:
\[ X = 4000 \]

### Step 4: Verify with Scheme B
Now, let's verify this with Scheme B, where the interest rate is \( 12\% \) per annum. The interest earned from Scheme B can be calculated similarly:
\[ \text{Interest from B} = \frac{X \times 12 \times 4}{100} = \frac{48X}{100} = 0.48X \]

The total amount after 4 years in Scheme B is:
\[ \text{Total Amount in B} = X + \text{Interest from B} = X + 0.48X = 1.48X \]
According to the problem, this total amount equals Rs 5920:
\[ 1.48X = 5920 \]

### Step 5: Solve for \( X \) from Scheme B
To find \( X \), we can rearrange the equation:
\[ X = \frac{5920}{1.48} \]

Calculating this gives:
\[ X = 4000 \]

### Conclusion
The sum invested in each scheme is Rs 4000.