In how much time (in years) will a sum of Rs. 9500 amounts to Rs. 17622.5 at the rate of 4.5 % per annum at simple interest ?

Options

A. 21
B. 23
C. 19
D. 20

Answer

To solve the problem of how much time it will take for a sum of Rs. 9500 to amount to Rs. 17622.5 at a rate of 4.5% per annum using simple interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 9500
- Amount (A) = Rs. 17622.5
- Rate of interest (R) = 4.5% per annum

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = A - P \]

Substituting the values:
\[ \text{SI} = 17622.5 - 9500 \]
\[ \text{SI} = 8122.5 \]

### Step 3: Use the Simple Interest formula to find time (T)
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

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

### Step 4: Substitute the known values into the formula
Substituting the values we have:
- SI = 8122.5
- P = 9500
- R = 4.5

So,
\[ T = \frac{8122.5 \times 100}{9500 \times 4.5} \]

### Step 5: Calculate the denominator
Calculating the denominator:
\[ 9500 \times 4.5 = 42750 \]

### Step 6: Calculate time (T)
Now substituting back into the time formula:
\[ T = \frac{8122.5 \times 100}{42750} \]
\[ T = \frac{812250}{42750} \]
\[ T = 19 \]

### Final Answer
Thus, the time required for the sum of Rs. 9500 to amount to Rs. 17622.5 at the rate of 4.5% per annum is **19 years**.

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