₹ 500 wasinvested at 12% per annum simpleinterest and a certain sum of money at 10% per annum simple interest. If the sum oftheinterests on both the sum after 4 years is ₹ 480, the other sum of money is:

Options

A. Rs 550
B. Rs 450
C. Rs 600
D. Rs 750

Answer

To solve the problem step-by-step, we will use the formula for simple interest and the information provided in the question.

### Step 1: Identify the given values
- Amount invested at 12% per annum (P1) = ₹500
- Rate of interest for the first amount (R1) = 12%
- Time period (T) = 4 years
- Total interest from both investments = ₹480
- Rate of interest for the second amount (R2) = 10%
- Amount invested at 10% per annum (P2) = x (unknown)

### Step 2: Calculate the interest from the first investment
Using the formula for simple interest:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]

For the first investment:
\[ \text{Interest from P1} = \frac{500 \times 12 \times 4}{100} \]
\[ = \frac{24000}{100} = ₹240 \]

### Step 3: Set up the equation for the total interest
The total interest from both investments is given as ₹480. Therefore, the interest from the second investment can be calculated as:
\[ \text{Interest from P2} = \text{Total Interest} - \text{Interest from P1} \]
\[ \text{Interest from P2} = 480 - 240 = ₹240 \]

### Step 4: Calculate the interest from the second investment
Using the simple interest formula for the second investment:
\[ \text{Interest from P2} = \frac{x \times 10 \times 4}{100} \]
Setting this equal to ₹240:
\[ \frac{x \times 10 \times 4}{100} = 240 \]

### Step 5: Simplify and solve for x
\[ \frac{40x}{100} = 240 \]
\[ 40x = 24000 \]
\[ x = \frac{24000}{40} = 600 \]

### Conclusion
The other sum of money (P2) is ₹600.