In what time will Rs. 7500 amount to Rs. 8625, if simple interest is reckoned at `7""1/2%` per annum?

Answer

To solve the problem step by step, we will follow the process of calculating the time it takes for Rs. 7500 to amount to Rs. 8625 at a simple interest rate of 7.5% per annum.

### Step 1: Identify the Given Values
- Principal (P) = Rs. 7500
- Amount (A) = Rs. 8625
- Rate of Interest (R) = 7.5% per annum

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

Substituting the values:
\[ \text{SI} = 8625 - 7500 \]
\[ \text{SI} = 1125 \]

### Step 3: Convert the Rate of Interest to a Fraction
The rate of interest is given as 7.5%. We can express this as a fraction:
\[ 7.5\% = \frac{15}{2}\% \]

### Step 4: Use the Simple Interest Formula
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( T \) = Time in years

Substituting the known values into the formula:
\[ 1125 = \frac{7500 \times \frac{15}{2} \times T}{100} \]

### Step 5: Simplify the Equation
To eliminate the fraction, we can multiply both sides by 100:
\[ 1125 \times 100 = 7500 \times \frac{15}{2} \times T \]
\[ 112500 = 7500 \times \frac{15}{2} \times T \]

### Step 6: Solve for Time (T)
Now, we need to isolate \( T \):
\[ T = \frac{112500}{7500 \times \frac{15}{2}} \]

Calculating the denominator:
\[ 7500 \times \frac{15}{2} = 7500 \times 7.5 = 56250 \]

Now substituting back:
\[ T = \frac{112500}{56250} \]

### Step 7: Simplify Further
Dividing both the numerator and denominator:
\[ T = 2 \]

### Conclusion
The time it will take for Rs. 7500 to amount to Rs. 8625 at a simple interest rate of 7.5% per annum is **2 years**.

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