If the simple interest for 5 years be equal to 25% of the principal, it will be equal to the principal after

Options

A. (a) 10 years
B. (b) 20 years
C. (c) 30 years
D. (d) 40 years

Answer

To solve the problem step by step, let's break down the information given and find the solution.

### Step 1: Understand the given information
We know that the simple interest (SI) for 5 years is equal to 25% of the principal (P).

### Step 2: Express simple interest in terms of principal
The simple interest for 5 years can be expressed as:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal
- \( R \) = Rate of interest
- \( T \) = Time in years

From the problem, we know:
\[ \text{SI} = 25\% \text{ of } P = \frac{P}{4} \]

### Step 3: Set up the equation
For 5 years, we can substitute \( T = 5 \) into the simple interest formula:
\[ \frac{P \times R \times 5}{100} = \frac{P}{4} \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
1. Cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{R \times 5}{100} = \frac{1}{4} \]
2. Multiply both sides by 100:
\[ R \times 5 = 25 \]
3. Divide both sides by 5:
\[ R = 5\% \]

### Step 5: Find when simple interest equals principal
Now we need to find out after how many years the simple interest will equal the principal. We set up the equation again:
\[ \text{SI} = P \]
Using the formula for simple interest:
\[ \frac{P \times R \times T}{100} = P \]

### Step 6: Substitute the rate
Substituting \( R = 5\% \):
\[ \frac{P \times 5 \times T}{100} = P \]

### Step 7: Simplify to find T
1. Cancel \( P \) from both sides:
\[ \frac{5T}{100} = 1 \]
2. Multiply both sides by 100:
\[ 5T = 100 \]
3. Divide both sides by 5:
\[ T = 20 \]

### Conclusion
The simple interest will equal the principal after **20 years**.

---