Aniket deposited two parts of a sum of 25000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year he got 4050 as the total interest. What was the amount deposited at the rate of 18% per annum?

Options

A. 10000
B. 18000
C. 15000
D. None of these

Answer

To solve the problem step by step, we need to find out how much Aniket deposited at the rate of 18% per annum.

### Step 1: Define the variables
Let:
- \( x \) = amount deposited at 15% per annum
- \( y \) = amount deposited at 18% per annum

From the problem, we know:
- \( x + y = 25000 \) (total amount deposited)

### Step 2: Set up the interest equation
The total interest earned from both deposits in one year is given as 4050. The interest from each deposit can be calculated as:
- Interest from \( x \) at 15% = \( \frac{15}{100} \times x \)
- Interest from \( y \) at 18% = \( \frac{18}{100} \times y \)

Thus, the total interest equation can be written as:
\[ \frac{15}{100} x + \frac{18}{100} y = 4050 \]

### Step 3: Simplify the interest equation
To eliminate the fractions, multiply the entire equation by 100:
\[ 15x + 18y = 405000 \]

### Step 4: Solve the system of equations
Now we have a system of two equations:
1. \( x + y = 25000 \)
2. \( 15x + 18y = 405000 \)

From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 25000 - x \]

Substituting \( y \) in the second equation:
\[ 15x + 18(25000 - x) = 405000 \]

### Step 5: Expand and simplify
Expanding the equation:
\[ 15x + 450000 - 18x = 405000 \]

Combine like terms:
\[ -3x + 450000 = 405000 \]

### Step 6: Isolate \( x \)
Subtract 450000 from both sides:
\[ -3x = 405000 - 450000 \]
\[ -3x = -45000 \]

Now, divide by -3:
\[ x = 15000 \]

### Step 7: Find \( y \)
Now substitute \( x \) back into the equation for \( y \):
\[ y = 25000 - 15000 = 10000 \]

### Step 8: Conclusion
The amount deposited at the rate of 18% per annum is \( y = 10000 \).

### Final Answer
The amount deposited at the rate of 18% per annum is **10,000**.

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