A sum of money doubles itself in 10 yr. In how many years would it triple itself?

Options

A. 20yr
B. 10yr
C. 30yr
D. None of these

Answer

To solve the problem of how long it will take for a sum of money to triple itself when it doubles in 10 years, we can follow these steps:

### Step 1: Understand the relationship between Principal, Amount, and Simple Interest
- Let the principal amount be \( P \).
- If the money doubles in 10 years, the amount after 10 years is \( 2P \).
- The formula for the amount \( A \) is given by:
\[ A = P + \text{SI} \]
where SI is the simple interest.

### Step 2: Write the formula for Simple Interest
- The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where \( R \) is the rate of interest and \( T \) is the time in years.

### Step 3: Set up the equation for the amount after 10 years
- After 10 years, the amount is:
\[ A = P + \frac{P \times R \times 10}{100} \]
- Since \( A = 2P \), we can set up the equation:
\[ 2P = P + \frac{P \times R \times 10}{100} \]

### Step 4: Simplify the equation
- Cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = 1 + \frac{R \times 10}{100} \]
- Rearranging gives:
\[ 2 - 1 = \frac{R \times 10}{100} \]
\[ 1 = \frac{R \times 10}{100} \]

### Step 5: Solve for the rate \( R \)
- Multiply both sides by 100:
\[ 100 = R \times 10 \]
- Divide by 10:
\[ R = 10\% \]

### Step 6: Set up the equation for tripling the amount
- Now we want to find out how long it will take for the amount to triple, which means \( A = 3P \).
- Using the same formula for the amount:
\[ 3P = P + \frac{P \times R \times T}{100} \]
- Cancel \( P \):
\[ 3 = 1 + \frac{R \times T}{100} \]

### Step 7: Substitute the value of \( R \) and solve for \( T \)
- Substitute \( R = 10\% \):
\[ 3 = 1 + \frac{10 \times T}{100} \]
- Rearranging gives:
\[ 3 - 1 = \frac{10T}{100} \]
\[ 2 = \frac{10T}{100} \]
- Multiply both sides by 100:
\[ 200 = 10T \]
- Divide by 10:
\[ T = 20 \text{ years} \]

### Conclusion
The sum of money will triple itself in **20 years**.

---