To solve the problem step by step, we will use the formula for simple interest and set up an equation based on the information given.
### Step 1: Identify the known values
- Investment 1: Rs 10,500 at x% per annum
- Investment 2: Rs 13,500 at (x + 2)% per annum
- Total interest earned in 3 years: Rs 7,650
### 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
- \( R \) = Rate of interest
- \( T \) = Time in years
### Step 3: Calculate the interest for both investments
1. For the first investment (Rs 10,500 at x% for 3 years):
\[
\text{SI}_1 = \frac{10,500 \times x \times 3}{100} = \frac{31,500x}{100} = 315.00x
\]
2. For the second investment (Rs 13,500 at (x + 2)% for 3 years):
\[
\text{SI}_2 = \frac{13,500 \times (x + 2) \times 3}{100} = \frac{40,500(x + 2)}{100} = 405.00(x + 2)
\]
### Step 4: Set up the equation for total interest
According to the problem, the total interest from both investments is Rs 7,650:
\[
\text{SI}_1 + \text{SI}_2 = 7,650
\]
Substituting the values we calculated:
\[
315.00x + 405.00(x + 2) = 7,650
\]
### Step 5: Simplify the equation
Expanding the equation:
\[
315.00x + 405.00x + 810.00 = 7,650
\]
Combine like terms:
\[
720.00x + 810.00 = 7,650
\]
### Step 6: Solve for x
Subtract 810 from both sides:
\[
720.00x = 7,650 - 810
\]
\[
720.00x = 6,840
\]
Now, divide both sides by 720:
\[
x = \frac{6,840}{720} = 9.5
\]
### Conclusion
The rate of interest on the first investment is **9.5%**.
