At some rate of simple interest, A lent Rs. 6000 to B for 2 years and Rs. 1500 to C for 4 years and received Rs. 900 as interest from both of them together. The rate of interest per annum was:

Options

A. a. `4%`
B. b. `8%`
C. c. `10%`
D. d. `5%`

Answer

To find the rate of interest per annum, we will use the formula for simple interest and set up an equation based on the information provided in the question.

### Step-by-Step Solution:

1. **Identify the amounts lent and the time periods**:
- Amount lent to B (P1) = Rs. 6000 for 2 years
- Amount lent to C (P2) = Rs. 1500 for 4 years

2. **Use the formula for Simple Interest (SI)**:
The formula for Simple Interest is:
\[ SI = \frac{P \times T \times R}{100} \]
where:
- \(P\) = Principal amount
- \(T\) = Time in years
- \(R\) = Rate of interest per annum

3. **Calculate the interest from both loans**:
- Interest from B (SI1):
\[ SI1 = \frac{6000 \times 2 \times R}{100} = \frac{12000R}{100} = 120R \]
- Interest from C (SI2):
\[ SI2 = \frac{1500 \times 4 \times R}{100} = \frac{6000R}{100} = 60R \]

4. **Set up the equation for total interest**:
According to the problem, the total interest received from both B and C is Rs. 900:
\[ SI1 + SI2 = 900 \]
Substituting the expressions for SI1 and SI2:
\[ 120R + 60R = 900 \]

5. **Combine like terms**:
\[ 180R = 900 \]

6. **Solve for R**:
\[ R = \frac{900}{180} = 5 \]

7. **Conclusion**:
The rate of interest per annum is **5%**.