Rajni and Mohini deposited Rs.3000 and Rs.4000 in a company at the rate of 10% per annum for 3 years and `2 1/2` years respectively. The difference of the amounts received by them will be

Options

A. 100
B. 1000
C. 900
D. 1100

Answer

To solve the problem step by step, we will calculate the simple interest for both Rajni and Mohini, find the total amounts they receive, and then determine the difference between those amounts.

### Step 1: Calculate Simple Interest for Rajni
1. **Identify the values**:
- Principal (P) = Rs. 3000
- Rate (R) = 10% per annum
- Time (T) = 3 years

2. **Use the formula for Simple Interest (SI)**:
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substitute the values**:
\[ SI = \frac{3000 \times 10 \times 3}{100} \]

4. **Calculate**:
\[ SI = \frac{30000}{100} = 300 \]
\[ SI = 900 \]

### Step 2: Calculate Total Amount Received by Rajni
1. **Use the formula**:
\[ \text{Total Amount} = P + SI \]

2. **Substitute the values**:
\[ \text{Total Amount} = 3000 + 900 = 3900 \]

### Step 3: Calculate Simple Interest for Mohini
1. **Identify the values**:
- Principal (P) = Rs. 4000
- Rate (R) = 10% per annum
- Time (T) = 2.5 years

2. **Use the formula for Simple Interest (SI)**:
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substitute the values**:
\[ SI = \frac{4000 \times 10 \times 2.5}{100} \]

4. **Calculate**:
\[ SI = \frac{100000}{100} = 1000 \]

### Step 4: Calculate Total Amount Received by Mohini
1. **Use the formula**:
\[ \text{Total Amount} = P + SI \]

2. **Substitute the values**:
\[ \text{Total Amount} = 4000 + 1000 = 5000 \]

### Step 5: Calculate the Difference in Amounts Received
1. **Identify the amounts**:
- Amount received by Rajni = Rs. 3900
- Amount received by Mohini = Rs. 5000

2. **Calculate the difference**:
\[ \text{Difference} = \text{Amount}_{\text{Mohini}} - \text{Amount}_{\text{Rajni}} \]
\[ \text{Difference} = 5000 - 3900 = 1100 \]

### Final Answer
The difference of the amounts received by Rajni and Mohini is Rs. 1100.

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