Simple intereset on a sum for 10 years is equal to 5 % of the principa. In how many years interest will be equal to the principal ?

Options

A. 100
B. 150
C. 200
D. 250

Answer

To solve the problem step by step, we will follow the information given in the question and apply the concept of simple interest.

### Step 1: Understand the given information
We know that the simple interest (SI) for 10 years is equal to 5% of the principal (P).

### Step 2: Set up the equation
Let the principal amount (P) be 100 (for simplicity). According to the problem:
- Simple Interest (SI) for 10 years = 5% of P
- SI for 10 years = (5/100) * 100 = 5

### Step 3: Calculate the rate of interest
Using the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest per annum
- T = Time in years

Substituting the known values into the formula:
\[ 5 = \frac{100 \times R \times 10}{100} \]
This simplifies to:
\[ 5 = R \times 10 \]
Now, solve for R:
\[ R = \frac{5}{10} = 0.5\% \]

### Step 4: Determine the time when interest equals the principal
We need to find out how many years (T) it will take for the simple interest to equal the principal amount (P). We set up the equation:
\[ SI = P \]
Substituting the SI formula:
\[ \frac{P \times R \times T}{100} = P \]
We can cancel P from both sides (assuming P ≠ 0):
\[ \frac{R \times T}{100} = 1 \]
Now substituting R = 0.5%:
\[ \frac{0.5 \times T}{100} = 1 \]
To solve for T, multiply both sides by 100:
\[ 0.5T = 100 \]
Now divide by 0.5:
\[ T = \frac{100}{0.5} = 200 \]

### Final Answer
The interest will be equal to the principal in **200 years**.

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