A person borrows some money for 4 years at the rate of simple interest. If the ratio of principal and total interest is 5 : 1, then what is the rate (in per cent per annum) of interest ?

Options

A. 5
B. 25
C. 10
D. 20

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the given information
We know that:
- The ratio of the principal (P) to the total interest (I) is given as 5:1.
- The time period (T) is 4 years.

### Step 2: Express the principal and interest in terms of a variable
Let the principal be represented as \( 5x \) and the total interest as \( x \), where \( x \) is a common factor.

### Step 3: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ I = P \times r \times T \]
Where:
- \( I \) is the interest,
- \( P \) is the principal,
- \( r \) is the rate of interest (in decimal),
- \( T \) is the time in years.

### Step 4: Substitute the known values into the formula
From our previous steps, we know:
- \( I = x \)
- \( P = 5x \)
- \( T = 4 \)

Substituting these into the formula gives:
\[ x = (5x) \times r \times 4 \]

### Step 5: Simplify the equation
Rearranging the equation:
\[ x = 20xr \]
To isolate \( r \), we can divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[ 1 = 20r \]

### Step 6: Solve for the rate of interest \( r \)
Now, solving for \( r \):
\[ r = \frac{1}{20} \]

### Step 7: Convert \( r \) to a percentage
To convert \( r \) into a percentage, we multiply by 100:
\[ \text{Rate} = r \times 100 = \frac{1}{20} \times 100 = 5\% \]

### Conclusion
The rate of interest is \( 5\% \) per annum.

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