A person deposited Rs 500 for 4 years and Rs 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs 190 as interest. The rate of simple interest per annum was

Options

A. 0.04
B. 0.05
C. 0.02
D. 0.03

Answer

To find the rate of simple interest per annum, we can break down the problem step by step.

### Step 1: Understand the formula for Simple Interest
The formula for calculating simple interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Calculate the interest for each deposit
1. **For the first deposit of Rs 500 for 4 years:**
\[ \text{SI}_1 = \frac{500 \times R \times 4}{100} = \frac{2000R}{100} = 20R \]

2. **For the second deposit of Rs 600 for 3 years:**
\[ \text{SI}_2 = \frac{600 \times R \times 3}{100} = \frac{1800R}{100} = 18R \]

### Step 3: Write the equation for total interest
According to the problem, the total interest received from both deposits is Rs 190. Therefore, we can write:
\[ \text{SI}_1 + \text{SI}_2 = 190 \]
Substituting the values we calculated:
\[ 20R + 18R = 190 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 38R = 190 \]

### Step 5: Solve for R
To find the rate \( R \), divide both sides by 38:
\[ R = \frac{190}{38} = 5 \]

### Conclusion
The rate of simple interest per annum is \( \mathbf{5\%} \).

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