A sum of money becomes triple of itself in 8 yr at SI. In twelve years it will become how many times of itself at the same rate?

Options

A. 6 times
B. 4 times
C. 5 times
D. None of the above

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Problem
We know that a sum of money becomes triple of itself in 8 years at simple interest (SI). We need to find out how many times it will become in 12 years at the same rate.

### Step 2: Define Variables
Let the principal amount be \( P \).
According to the problem, the amount after 8 years is \( 3P \).

### Step 3: Calculate Simple Interest
The simple interest (SI) can be calculated as:
\[ \text{SI} = \text{Amount} - \text{Principal} = 3P - P = 2P \]

### Step 4: Use the Simple Interest Formula
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the principal,
- \( R \) is the rate of interest,
- \( T \) is the time in years.

From our previous calculation, we know:
\[ 2P = \frac{P \times R \times 8}{100} \]

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

### Step 6: Solve for Rate \( R \)
Rearranging the equation gives:
\[ R = \frac{2 \times 100}{8} = 25\% \]

### Step 7: Calculate Simple Interest for 12 Years
Now, we will calculate the simple interest for 12 years using the same rate:
\[ \text{SI}_{12} = \frac{P \times R \times 12}{100} = \frac{P \times 25 \times 12}{100} \]
\[ = \frac{300P}{100} = 3P \]

### Step 8: Calculate the Amount after 12 Years
The total amount after 12 years will be:
\[ \text{Amount}_{12} = \text{Principal} + \text{SI}_{12} = P + 3P = 4P \]

### Step 9: Determine How Many Times the Principal
To find out how many times the principal this amount is:
\[ \text{Times} = \frac{\text{Amount}_{12}}{P} = \frac{4P}{P} = 4 \]

### Conclusion
Thus, the sum of money will become **4 times** of itself in 12 years.

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