The simple interest on a sum of money in 12 years is three times of the principal. Find the rate of interest.

Options

A. `13(1)/(3)%`
B. `25%`
C. `6(2)/(3)%`
D. `10%`

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the relationship between Principal (P), Rate of Interest (R), and Time (T).

### Step 1: Understand the relationship between Simple Interest, Principal, Rate, and Time
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = 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 (SI) for 12 years is three times the Principal (P):
\[ SI = 3P \]
Since the time \(T\) is given as 12 years, we can substitute this into the SI formula:
\[ 3P = \frac{P \times R \times 12}{100} \]

### Step 3: Simplify the equation
We can cancel \(P\) from both sides (assuming \(P \neq 0\)):
\[ 3 = \frac{R \times 12}{100} \]

### Step 4: Solve for the Rate of Interest (R)
To isolate \(R\), we can multiply both sides by 100:
\[ 300 = R \times 12 \]
Now, divide both sides by 12:
\[ R = \frac{300}{12} \]
Calculating this gives:
\[ R = 25 \]

### Step 5: State the final answer
Thus, the rate of interest is:
\[ \text{Rate of Interest} = 25\% \]