At the same rate of simple interest sum of the interest of Rs 300 for 4 years and the interest of Rs 400 for 3 years is Rs 120. The rate of interest is

Options

A. 0.05
B. 0.04
C. 0.06
D. 0.1

Answer

To find the rate of interest, we can use the formula for simple interest, which is:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

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

Given:
- The principal amount for the first case is Rs 300, time is 4 years.
- The principal amount for the second case is Rs 400, time is 3 years.
- The total interest from both cases is Rs 120.

### Step 1: Write the equations for both cases of interest.

For the first principal:
\[ \text{SI}_1 = \frac{300 \times R \times 4}{100} \]

For the second principal:
\[ \text{SI}_2 = \frac{400 \times R \times 3}{100} \]

### Step 2: Combine the two interest equations.

The total interest from both cases is given as Rs 120:
\[ \text{SI}_1 + \text{SI}_2 = 120 \]

Substituting the equations from Step 1:
\[ \frac{300 \times R \times 4}{100} + \frac{400 \times R \times 3}{100} = 120 \]

### Step 3: Simplify the equation.

Multiply through by 100 to eliminate the denominator:
\[ 300 \times R \times 4 + 400 \times R \times 3 = 12000 \]

Calculating the left side:
\[ 1200R + 1200R = 12000 \]

Combine like terms:
\[ 2400R = 12000 \]

### Step 4: Solve for \( R \).

Now, divide both sides by 2400:
\[ R = \frac{12000}{2400} \]

Calculating the right side:
\[ R = 5 \]

### Step 5: Interpret the result.

Since \( R \) is the rate of interest, we can express it as a percentage:
\[ R = 5\% \]

### Final Answer:
The rate of interest is **5%**.

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