Madhulika 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. 4050 as the total interest. What was the amount deposited at the rate of 15% per annum ?

Options

A. Rs. 10,000
B. Rs. 15,000
C. Rs. 9,000
D. Data inadequate

Answer

To solve the problem step by step, we will use the information provided to find out how much Madhulika deposited at the rate of 15% per annum.

### Step 1: Understand the Total Amount and Interest
Madhulika has a total amount of Rs. 25,000 deposited in two parts at different interest rates (15% and 18%). The total interest earned in one year is Rs. 4,050.

**Hint:** Identify the total amount and total interest to set up the problem.

### Step 2: Calculate the Effective Interest Rate
To find the effective interest rate, we can use the formula:
\[ \text{Effective Interest Rate} = \frac{\text{Total Interest}}{\text{Total Amount}} \times 100 \]
Substituting the values:
\[ \text{Effective Interest Rate} = \frac{4050}{25000} \times 100 = 16.2\% \]

**Hint:** Calculate the effective interest rate to understand the average return on the total investment.

### Step 3: Set Up the Alligation Method
We can use the alligation method to find the ratio of the amounts deposited at the two different rates. The effective interest rate (16.2%) is between the two rates (15% and 18%).

- Rate 1 (15%) is lower than the effective rate (16.2%).
- Rate 2 (18%) is higher than the effective rate (16.2%).

Using alligation:
\[ \text{Difference from 15%} = 16.2 - 15 = 1.2 \]
\[ \text{Difference from 18%} = 18 - 16.2 = 1.8 \]

**Hint:** Use the alligation method to find the ratio of the two parts deposited.

### Step 4: Find the Ratio of the Deposits
The ratio of the amounts deposited at 15% and 18% can be expressed as:
\[ \text{Ratio} = \frac{1.8}{1.2} = \frac{3}{2} \]

**Hint:** Simplify the differences to find the ratio of the amounts deposited.

### Step 5: Calculate the Total Parts and Individual Deposits
The total parts in the ratio is \(3 + 2 = 5\). Let the amount deposited at 15% be \(3x\) and at 18% be \(2x\).

Since the total amount deposited is Rs. 25,000:
\[ 3x + 2x = 25000 \]
\[ 5x = 25000 \]
\[ x = 5000 \]

**Hint:** Set up an equation based on the ratio to find the value of \(x\).

### Step 6: Find the Amount Deposited at 15%
Now, we can find the amount deposited at 15%:
\[ \text{Amount at 15%} = 3x = 3 \times 5000 = 15000 \]

**Hint:** Multiply the value of \(x\) by the ratio part to find the individual deposit amounts.

### Conclusion
Madhulika deposited Rs. 15,000 at the rate of 15% per annum.

**Final Answer:** Rs. 15,000