In what time will the simple interest be2/5 of the principal at 8 per cent per annum?

Options

A. 8 years
B. 7 years
C. 5 years
D. 6 years

Answer

To solve the problem of finding the time when the simple interest is \( \frac{2}{5} \) of the principal at an interest rate of 8% per annum, we can follow these steps:

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

### Step 2: Set up the equation based on the problem statement
According to the problem, the Simple Interest is \( \frac{2}{5} \) of the Principal. Let’s denote the Principal as \( P \). Therefore, we can write:
\[ SI = \frac{2}{5} P \]

### Step 3: Substitute the values into the Simple Interest formula
Now, substituting the values into the formula, we have:
\[ \frac{2}{5} P = \frac{P \times 8 \times T}{100} \]

### Step 4: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{2}{5} = \frac{8 \times T}{100} \]

### Step 5: Cross-multiply to solve for \( T \)
Cross-multiplying gives us:
\[ 2 \times 100 = 5 \times 8 \times T \]
\[ 200 = 40T \]

### Step 6: Solve for \( T \)
Now, divide both sides by 40 to isolate \( T \):
\[ T = \frac{200}{40} = 5 \]

### Conclusion
The time required for the Simple Interest to be \( \frac{2}{5} \) of the Principal at 8% per annum is **5 years**.

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