15,000 amounts to Rs 25,800 in 8 years at simple interest. The rate of interest will be:

Options

A. `5(1)/(2)%`
B. 0.09
C. 0.1
D. 0.11

Answer

To find the rate of interest when Rs 15,000 amounts to Rs 25,800 in 8 years at simple interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 15,000
- Amount (A) = Rs 25,800
- Time (T) = 8 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:
\[ \text{SI} = 25,800 - 15,000 = 10,800 \]

### Step 3: Use the Simple Interest formula to find the rate
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
- T = Time in years

We can rearrange this formula to solve for R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ R = \frac{10,800 \times 100}{15,000 \times 8} \]

### Step 5: Calculate R
First, calculate the denominator:
\[ 15,000 \times 8 = 120,000 \]
Now substitute this back into the equation:
\[ R = \frac{10,800 \times 100}{120,000} \]
\[ R = \frac{1,080,000}{120,000} \]
Now simplify:
\[ R = 9 \]

### Step 6: Conclusion
The rate of interest (R) is 9%.