If the simple interest for 6 years be equal to 30 % of the principal, it will be equal to the principal after

Options

A. 10 years
B. 20 years
C. 22 years
D. 30 years

Answer

To solve the problem step by step, we will follow the given information and apply the formula for simple interest.

### Step 1: Understand the relationship between Simple Interest (SI) and Principal (P)
We know that the Simple Interest (SI) for a certain time period can be calculated using the formula:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set up the equation based on the problem statement
According to the question, the Simple Interest for 6 years is equal to 30% of the Principal. Therefore, we can write:
\[ \text{SI} = \frac{P \times R \times 6}{100} = \frac{30}{100} \times P \]

### Step 3: Simplify the equation
Now, we can simplify the equation by canceling \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{R \times 6}{100} = \frac{30}{100} \]
This simplifies to:
\[ R \times 6 = 30 \]

### Step 4: Solve for the Rate of Interest (R)
Now, we can solve for \( R \):
\[ R = \frac{30}{6} = 5\% \]

### Step 5: Find out after how many years the Simple Interest will equal the Principal
We need to find out after how many years (let's call it \( T_1 \)) the Simple Interest will equal the Principal. This means:
\[ \text{SI} = P \]
Using the Simple Interest formula:
\[ P = \frac{P \times R \times T_1}{100} \]
Again, we can cancel \( P \) from both sides:
\[ 1 = \frac{R \times T_1}{100} \]

### Step 6: Substitute the value of R and solve for T1
Substituting \( R = 5\% \):
\[ 1 = \frac{5 \times T_1}{100} \]
Now, multiply both sides by 100:
\[ 100 = 5 \times T_1 \]
Now, divide both sides by 5:
\[ T_1 = \frac{100}{5} = 20 \text{ years} \]

### Final Answer
Thus, the Simple Interest will be equal to the Principal after **20 years**.

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