If a Sum of money doubles itself in 7 years, it becomes 5 times in how many years?

Options

A. a. 20 Years
B. b. 28 Years
C. c. 36 Years
D. d. None of the above

Answer

To solve the problem of how long it takes for a sum of money to become five times its original amount when it doubles in seven years, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
- Let the principal amount (initial sum of money) be \( P = X \).
- The time taken to double the money is given as \( T = 7 \) years.

2. **Calculate the Simple Interest (SI) for Doubling**:
- When the money doubles, the final amount becomes \( 2P = 2X \).
- The simple interest earned in this time is:
\[ SI = 2X - X = X \]

3. **Use the Simple Interest Formula**:
- The formula for simple interest is:
\[ SI = \frac{P \cdot R \cdot T}{100} \]
- Substituting the known values into the formula:
\[ X = \frac{X \cdot R \cdot 7}{100} \]

4. **Solve for the Rate (R)**:
- Cancel \( X \) from both sides (assuming \( X \neq 0 \)):
\[ 1 = \frac{R \cdot 7}{100} \]
- Rearranging gives:
\[ R = \frac{100}{7} \text{ percent} \]

5. **Determine the Simple Interest for Five Times the Principal**:
- When the amount becomes five times the principal, the final amount is \( 5P = 5X \).
- The simple interest earned in this case is:
\[ SI = 5X - X = 4X \]

6. **Set Up the Simple Interest Formula Again**:
- Using the simple interest formula with the new values:
\[ 4X = \frac{X \cdot \left(\frac{100}{7}\right) \cdot T}{100} \]

7. **Simplify the Equation**:
- Cancel \( X \) from both sides:
\[ 4 = \frac{100}{7} \cdot T \]
- Rearranging gives:
\[ T = \frac{4 \cdot 7}{100} = \frac{28}{1} = 28 \text{ years} \]

8. **Final Answer**:
- It takes **28 years** for the sum of money to become five times its original amount.