Rs 500 was inversted at 12 % per annum simple interset and a certain sum of money inversted at 10 % per annum simple interset. If the sum of the interset on both the sum after 4 years is Rs 480, the latter sum of money is :

Options

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

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
We have two investments:
1. Rs 500 invested at 12% per annum.
2. A certain sum (let's call it Rs x) invested at 10% per annum.

The total interest earned from both investments after 4 years is Rs 480.

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 3: Calculate the interest from the first investment
For the first investment of Rs 500 at 12% for 4 years:
\[ \text{SI}_1 = \frac{500 \times 12 \times 4}{100} \]

### Step 4: Calculate the interest from the second investment
For the second investment of Rs x at 10% for 4 years:
\[ \text{SI}_2 = \frac{x \times 10 \times 4}{100} \]

### Step 5: Set up the equation
According to the problem, the total interest from both investments is Rs 480:
\[ \text{SI}_1 + \text{SI}_2 = 480 \]
Substituting the values we calculated:
\[ \frac{500 \times 12 \times 4}{100} + \frac{x \times 10 \times 4}{100} = 480 \]

### Step 6: Simplify the equation
Calculating the first part:
\[ \frac{500 \times 12 \times 4}{100} = \frac{24000}{100} = 240 \]
So, we have:
\[ 240 + \frac{x \times 40}{100} = 480 \]

### Step 7: Isolate the second investment's interest
Subtract 240 from both sides:
\[ \frac{x \times 40}{100} = 480 - 240 \]
\[ \frac{x \times 40}{100} = 240 \]

### Step 8: Solve for x
Multiply both sides by 100:
\[ x \times 40 = 24000 \]
Now divide by 40:
\[ x = \frac{24000}{40} \]
\[ x = 600 \]

### Conclusion
The latter sum of money invested at 10% per annum is Rs 600.

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