At the rate of 12.5% per annum, the simple interest on a sum is 5/4 of the principal. What is the time period (in years)?

Options

A. `12.5`
B. 8
C. 10
D. 15

Answer

To solve the problem step by step, we will use the formula for simple interest and the information provided in the question.

### Step 1: Understand the given information
- Rate of interest (r) = 12.5% per annum
- Simple Interest (SI) = \( \frac{5}{4} \) of the Principal (P)

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest is given by:
\[ SI = \frac{P \times r \times t}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( r \) = Rate of interest
- \( t \) = Time period in years

### Step 3: Substitute the values into the formula
From the problem, we know that:
\[ SI = \frac{5}{4} P \]
Substituting this into the formula, we get:
\[ \frac{5}{4} P = \frac{P \times 12.5 \times t}{100} \]

### Step 4: Cancel the Principal (P) from both sides
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ \frac{5}{4} = \frac{12.5 \times t}{100} \]

### Step 5: Solve for time (t)
Now, we can rearrange the equation to solve for \( t \):
\[ t = \frac{5}{4} \times \frac{100}{12.5} \]

### Step 6: Simplify the expression
Calculating \( \frac{100}{12.5} \):
\[ \frac{100}{12.5} = 8 \]
Now substituting back:
\[ t = \frac{5}{4} \times 8 \]
Calculating \( \frac{5 \times 8}{4} \):
\[ t = \frac{40}{4} = 10 \]

### Conclusion
The time period \( t \) is 10 years.