In what time will ₹8000 amount to ₹8360 at 6% per annum simple interest?

Options

A. `8 months `
B. `9 months `
C. `1.1/4 years`
D. `1.1/2 years`

Answer

To solve the problem of finding the time it will take for ₹8000 to amount to ₹8360 at a simple interest rate of 6% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal (P) = ₹8000
- Amount (A) = ₹8360
- Rate of interest (R) = 6% per annum

2. **Calculate the Simple Interest (SI)**:
- The formula for Simple Interest is:
\[ SI = A - P \]
- Substitute the values:
\[ SI = 8360 - 8000 = ₹360 \]

3. **Use the Simple Interest formula to find time (T)**:
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Rearranging the formula to find time (T):
\[ T = \frac{SI \times 100}{P \times R} \]

4. **Substitute the values into the formula**:
- Substitute SI = ₹360, P = ₹8000, and R = 6%:
\[ T = \frac{360 \times 100}{8000 \times 6} \]

5. **Simplify the equation**:
- Calculate the denominator:
\[ 8000 \times 6 = 48000 \]
- Now substitute this back into the equation for T:
\[ T = \frac{36000}{48000} \]

6. **Further simplify the fraction**:
- Divide both the numerator and denominator by 12000:
\[ T = \frac{3}{4} \]

7. **Convert to years**:
- Since T = 0.75 years, we can express this as:
\[ T = 0.75 \text{ years} \]

### Final Answer:
The time it will take for ₹8000 to amount to ₹8360 at 6% per annum simple interest is **0.75 years**.