A lent Rs. 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest per

Options

A. 0.07
B. 0.05
C. `7(1)/(8)%`
D. 0.1

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI), which is:

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) is the principal amount
- \( R \) is the rate of interest per annum
- \( T \) is the time in years

### Step 1: Identify the given values
- Amount lent to B (P1) = Rs. 5000
- Time for B (T1) = 2 years
- Amount lent to C (P2) = Rs. 3000
- Time for C (T2) = 4 years
- Total interest received from both = Rs. 2200

### Step 2: Write the interest formulas for both loans
The interest from B can be calculated as:
\[ \text{SI}_1 = \frac{P_1 \times R \times T_1}{100} = \frac{5000 \times R \times 2}{100} = \frac{10000R}{100} = 100R \]

The interest from C can be calculated as:
\[ \text{SI}_2 = \frac{P_2 \times R \times T_2}{100} = \frac{3000 \times R \times 4}{100} = \frac{12000R}{100} = 120R \]

### Step 3: Set up the equation for total interest
According to the problem, the total interest from both loans is Rs. 2200. Therefore, we can write:
\[ \text{SI}_1 + \text{SI}_2 = 2200 \]
Substituting the values we found:
\[ 100R + 120R = 2200 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 220R = 2200 \]

### Step 5: Solve for R
To find the rate of interest \( R \), divide both sides by 220:
\[ R = \frac{2200}{220} = 10 \]

### Conclusion
The rate of interest per annum is **10%**.

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