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 `:`

Answer

To solve the problem step by step, we will calculate the rate of simple interest per annum based on the given deposits and the total interest received.

### Step 1: Understand the problem
We have two deposits:
- Rs. 500 for 4 years
- Rs. 600 for 3 years

The total interest received from both deposits is Rs. 190.

### Step 2: Set up the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate the interest for each deposit
1. For the first deposit of Rs. 500 for 4 years:
\[ SI_1 = \frac{500 \times R \times 4}{100} = \frac{2000R}{100} = 20R \]

2. For the second deposit of Rs. 600 for 3 years:
\[ SI_2 = \frac{600 \times R \times 3}{100} = \frac{1800R}{100} = 18R \]

### Step 4: Set up the equation for total interest
The total interest from both deposits is given as Rs. 190:
\[ SI_1 + SI_2 = 190 \]
Substituting the values we calculated:
\[ 20R + 18R = 190 \]

### Step 5: Combine like terms
Combine the terms on the left side:
\[ 38R = 190 \]

### Step 6: Solve for R
To find the rate \( R \), divide both sides by 38:
\[ R = \frac{190}{38} \]
Calculating this gives:
\[ R = 5 \]

### Step 7: Conclusion
The rate of simple interest per annum is:
\[ \text{Rate} = 5\% \]