In what rate of percent Rs. 800 becomes 836 in `3/4` years?

Options

A. 0.06
B. 0.07
C. 0.05
D. 0.12

Answer

To find the rate of interest at which Rs. 800 becomes Rs. 836 in \( \frac{3}{4} \) years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 800
- Amount (A) = Rs. 836
- Time (T) = \( \frac{3}{4} \) years

### Step 2: Calculate the Simple Interest (SI)
Simple Interest can be calculated using the formula:
\[ \text{SI} = \text{A} - \text{P} \]
Substituting the values:
\[ \text{SI} = 836 - 800 = 36 \]

### Step 3: Use the Simple Interest formula
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest (in percent)
- T = Time (in years)

### Step 4: Substitute the known values into the formula
We know:
- SI = 36
- P = 800
- T = \( \frac{3}{4} \)

Now substituting these values into the formula:
\[ 36 = \frac{800 \times R \times \frac{3}{4}}{100} \]

### Step 5: Simplify the equation
First, simplify the fraction:
\[ 36 = \frac{800 \times R \times 0.75}{100} \]
\[ 36 = \frac{600R}{100} \]
\[ 36 = 6R \]

### Step 6: Solve for R
To find R, divide both sides by 6:
\[ R = \frac{36}{6} = 6 \]

### Step 7: Conclusion
The rate of interest is \( R = 6\% \).