The simple interset on a sum for 5 years is `3/5` of the sum. The rate per cent per annum is

Options

A. `8%`
B. `10%`
C. `12%`
D. `12.1/2%`

Answer

To solve the problem step by step, we will follow the logic provided in the video transcript.

### Step 1: Define the Variables
Let the principal amount (the sum) be represented as \( X \).

### Step 2: Write the Simple Interest
According to the problem, the simple interest (SI) for 5 years is \( \frac{3}{5} \) of the principal amount. Therefore, we can write:
\[ SI = \frac{3}{5} X \]

### Step 3: Identify the Time
The time period given in the question is 5 years. So, we can denote:
\[ T = 5 \text{ years} \]

### Step 4: Recall the Simple Interest Formula
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

### Step 5: Substitute Known Values into the Formula
Substituting the known values into the formula, we have:
\[ \frac{3}{5} X = \frac{X \times R \times 5}{100} \]

### Step 6: Simplify the Equation
To simplify, we can multiply both sides by 100 to eliminate the fraction:
\[ 100 \times \frac{3}{5} X = X \times R \times 5 \]
This simplifies to:
\[ 60X = 5XR \]

### Step 7: Divide Both Sides by \( X \)
Assuming \( X \neq 0 \), we can divide both sides by \( X \):
\[ 60 = 5R \]

### Step 8: Solve for \( R \)
Now, divide both sides by 5 to find \( R \):
\[ R = \frac{60}{5} = 12 \]

### Conclusion
Thus, the rate of interest per annum is:
\[ \text{Rate} = 12\% \]

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