How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Options

A. 3.5 years
B. 4 years
C. 4.5 years
D. 5 years

Answer

To solve the problem of how much time it will take for an amount of Rs. 450 to yield Rs. 81 as interest at a rate of 4.5% per annum using simple interest, we can follow these steps:

### Step 1: Understand the formula for Simple Interest
The formula for calculating time (T) in simple interest is given by:
\[ T = \frac{100 \times I}{P \times R} \]
Where:
- \( I \) = Interest earned
- \( P \) = Principal amount (initial amount)
- \( R \) = Rate of interest per annum

### Step 2: Identify the values from the question
From the question, we have:
- Principal \( P = 450 \) Rs
- Interest \( I = 81 \) Rs
- Rate of interest \( R = 4.5\% \)

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ T = \frac{100 \times 81}{450 \times 4.5} \]

### Step 4: Calculate the denominator
First, calculate \( 450 \times 4.5 \):
\[ 450 \times 4.5 = 2025 \]

### Step 5: Substitute back into the formula
Now substitute back into the formula:
\[ T = \frac{100 \times 81}{2025} \]

### Step 6: Calculate the numerator
Calculate \( 100 \times 81 \):
\[ 100 \times 81 = 8100 \]

### Step 7: Divide the numerator by the denominator
Now divide \( 8100 \) by \( 2025 \):
\[ T = \frac{8100}{2025} \]

### Step 8: Simplify the fraction
To simplify \( \frac{8100}{2025} \), we can divide both the numerator and the denominator by 2025:
\[ T = 4 \]

### Final Answer
Thus, the time it will take for Rs. 450 to yield Rs. 81 as interest at 4.5% per annum is **4 years**.

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