The simple interest on a sum is `(3)/(5)` th of the principal at the rate of 7.5 % per annum. What is the time peroid (in years) ?

Options

A. 7.5
B. 8
C. 10
D. 12.5

Answer

To solve the problem step by step, we need to find the time period (in years) for which the simple interest is \( \frac{3}{5} \) of the principal at a rate of 7.5% per annum.

### Step 1: Understand the formula for Simple Interest
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time period in years

### Step 2: Set up the equation
According to the problem, the Simple Interest is \( \frac{3}{5} \) of the principal \( P \). Therefore, we can write:
\[ SI = \frac{3}{5} P \]

### Step 3: Substitute the values into the SI formula
Now, substituting \( SI \) into the Simple Interest formula:
\[ \frac{3}{5} P = \frac{P \times 7.5 \times T}{100} \]

### Step 4: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{3}{5} = \frac{7.5 \times T}{100} \]

### Step 5: Cross-multiply to solve for \( T \)
Cross-multiplying gives us:
\[ 3 \times 100 = 5 \times 7.5 \times T \]
\[ 300 = 37.5 T \]

### Step 6: Isolate \( T \)
Now, to isolate \( T \), we divide both sides by 37.5:
\[ T = \frac{300}{37.5} \]

### Step 7: Calculate \( T \)
Calculating the right side:
\[ T = 8 \]

### Conclusion
The time period \( T \) is 8 years.