Priya deposited two parts of a sum of Rs 25.000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year she got Rs 4.050 as the total interest. What was the amount deposited at the rate of 15% per annum ?

Options

A. 12000
B. 15000
C. 16,00
D. 10000

Answer

To solve the problem, we need to find the amount Priya deposited at the rate of 15% per annum. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( X \) = amount deposited at 15% per annum
- \( 25000 - X \) = amount deposited at 18% per annum

### Step 2: Write the Interest Formula
The total interest earned from both deposits in one year is given as Rs 4,050. The interest from each deposit can be calculated using the formula for simple interest:
\[ \text{Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]
For the amounts deposited:
- Interest from the amount at 15%:
\[ \frac{X \times 15 \times 1}{100} = \frac{15X}{100} \]
- Interest from the amount at 18%:
\[ \frac{(25000 - X) \times 18 \times 1}{100} = \frac{18(25000 - X)}{100} \]

### Step 3: Set Up the Equation
Now, we can set up the equation for the total interest:
\[ \frac{15X}{100} + \frac{18(25000 - X)}{100} = 4050 \]

### Step 4: Simplify the Equation
Multiply the entire equation by 100 to eliminate the denominators:
\[ 15X + 18(25000 - X) = 405000 \]
Expanding the equation:
\[ 15X + 450000 - 18X = 405000 \]

### Step 5: Combine Like Terms
Combine the \( X \) terms:
\[ -3X + 450000 = 405000 \]
Now, isolate \( X \):
\[ -3X = 405000 - 450000 \]
\[ -3X = -45000 \]

### Step 6: Solve for \( X \)
Divide by -3:
\[ X = \frac{-45000}{-3} = 15000 \]

### Conclusion
The amount deposited at the rate of 15% per annum is **Rs 15,000**.