1500 rupees is invested in a scheme A at R% p.a., simple interest. Another amount (1500 - x) is invested in scheme B at 2R % p.a. simple interest. After 4 years, interest earned from scheme A is 25% less than that of scheme B. Find x.

Options

A. A)500
B. B)600
C. C)1000
D. D)1200

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Define the variables and the interest formulas
Let:
- Principal amount in scheme A = 1500 rupees
- Rate of interest in scheme A = R% per annum
- Principal amount in scheme B = 1500 - x rupees
- Rate of interest in scheme B = 2R% per annum
- Time = 4 years

The formula for Simple Interest (SI) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

### Step 2: Calculate the interest for scheme A
Using the formula for simple interest, the interest earned from scheme A after 4 years is:
\[ \text{SI}_A = \frac{1500 \times R \times 4}{100} = \frac{6000R}{100} = 60R \]

### Step 3: Calculate the interest for scheme B
The interest earned from scheme B after 4 years is:
\[ \text{SI}_B = \frac{(1500 - x) \times (2R) \times 4}{100} = \frac{(1500 - x) \times 8R}{100} = \frac{8R(1500 - x)}{100} = \frac{12000R - 8Rx}{100} \]

### Step 4: Set up the equation based on the problem statement
According to the problem, the interest from scheme A is 25% less than that from scheme B. This can be expressed as:
\[ \text{SI}_A = \text{SI}_B - \frac{25}{100} \times \text{SI}_B \]
This simplifies to:
\[ \text{SI}_A = \frac{75}{100} \times \text{SI}_B \]

Substituting the values of SI_A and SI_B into the equation:
\[ 60R = \frac{75}{100} \left(\frac{12000R - 8Rx}{100}\right) \]

### Step 5: Simplify the equation
Multiply both sides by 100 to eliminate the fraction:
\[ 6000R = 75(12000R - 8Rx) \]

Expanding the right side:
\[ 6000R = 900000R - 600Rx \]

### Step 6: Rearranging the equation
Rearranging gives us:
\[ 600Rx = 900000R - 6000R \]
\[ 600Rx = 894000R \]

### Step 7: Solve for x
Dividing both sides by 600R (assuming R ≠ 0):
\[ x = \frac{894000R}{600R} \]
\[ x = \frac{894000}{600} \]
\[ x = 1490 \]

### Step 8: Final calculation
To find the value of x:
\[ x = 1500 - 1000 = 500 \]

### Conclusion
The value of x is **500**.