Akul lent ₹ 6000 to Bakul for 2 years and ₹ 1500 to camlin for 4 years and received altogether from both ₹ 900 as simple interest. The rate of interest is :

Options

A. `4%`
B. `8%`
C. `10%`
D. `5%`

Answer

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

\[ \text{Simple Interest (SI)} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]

### Step 1: Identify the Principal Amounts and Time Periods
- Akul lent ₹6000 to Bakul for 2 years.
- Akul lent ₹1500 to Kamlin for 4 years.

### Step 2: Set Up the Equation for Simple Interest
Let the rate of interest be \( x \% \).

The simple interest from Bakul can be calculated as:
\[ SI_{Bakul} = \frac{6000 \times x \times 2}{100} = \frac{12000x}{100} = 120x \]

The simple interest from Kamlin can be calculated as:
\[ SI_{Kamlin} = \frac{1500 \times x \times 4}{100} = \frac{6000x}{100} = 60x \]

### Step 3: Combine the Interests
According to the problem, the total simple interest received from both is ₹900. Therefore, we can set up the equation:
\[ 120x + 60x = 900 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 180x = 900 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 180:
\[ x = \frac{900}{180} = 5 \]

### Conclusion
The rate of interest is \( 5\% \).

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