A lent Rs. 6500 to B for 2 years and Rs. 8000 to C for 4 years at the same rate of simple interset and earned Rs. 4500 as interset from both amounts. The rate of interset per annum is :

Options

A. 0.08
B. 0.05
C. 0.1
D. 0.07

Answer

To find the rate of interest per annum, we can follow these steps:

### Step 1: Write the formula for Simple Interest
The formula for Simple Interest (SI) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Calculate Simple Interest for both loans
1. For the amount lent to B:
- Principal \( P_1 = 6500 \)
- Time \( T_1 = 2 \) years
- Simple Interest \( SI_1 = \frac{6500 \times R \times 2}{100} = \frac{13000R}{100} = 130R \)

2. For the amount lent to C:
- Principal \( P_2 = 8000 \)
- Time \( T_2 = 4 \) years
- Simple Interest \( SI_2 = \frac{8000 \times R \times 4}{100} = \frac{32000R}{100} = 320R \)

### Step 3: Set up the equation for total interest
According to the problem, the total interest earned from both loans is Rs. 4500. Therefore, we can write:
\[ SI_1 + SI_2 = 4500 \]
Substituting the expressions for \( SI_1 \) and \( SI_2 \):
\[ 130R + 320R = 4500 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 450R = 4500 \]

### Step 5: Solve for \( R \)
To find \( R \), divide both sides by 450:
\[ R = \frac{4500}{450} = 10 \]

### Step 6: Conclusion
Thus, the rate of interest per annum is:
\[ R = 10\% \]

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