The rate on which the amount of Rs 17,500 on simple interest for 2 years will be Rs 19,250:

Options

A. 12`1//2 %`
B. `10 %`
C. `7 ""1//2%`
D. `5%`

Answer

To find the rate of interest on a principal amount of Rs 17,500 that grows to Rs 19,250 in 2 years using simple interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 17,500
- Amount (A) = Rs 19,250
- Time (T) = 2 years

### Step 2: Calculate the Simple Interest (SI)
To find the simple interest, we use the formula:
\[ \text{SI} = A - P \]
Substituting the values:
\[ \text{SI} = 19,250 - 17,500 = 1,750 \]

### 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 (which we need to find)
- T = Time in years

### Step 4: Substitute the known values into the formula
We know:
- SI = 1,750
- P = 17,500
- T = 2 years

So, substituting these values into the formula:
\[ 1,750 = \frac{17,500 \times R \times 2}{100} \]

### Step 5: Simplify the equation
To eliminate the fraction, multiply both sides by 100:
\[ 1,750 \times 100 = 17,500 \times R \times 2 \]
\[ 175,000 = 35,000R \]

### Step 6: Solve for R
Now, divide both sides by 35,000 to find R:
\[ R = \frac{175,000}{35,000} \]
\[ R = 5 \]

### Step 7: Conclusion
The rate of interest is:
\[ R = 5\% \]