For every question, four probable answers bear in letters (A), (B), (C) and (D) are given. Only one out of these is correct. You have to choose the orrect answer.
In how much time an amount doubles at the rate of 20%?

Options

A. 4 years
B. 8 years
C. 10 years
D. 5 years

Answer

To solve the problem of how much time it takes for an amount to double at a rate of 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find out how long it takes for an initial amount (Principal, P) to double (become 2P) at an interest rate of 20%.

2. **Formula for Simple Interest**: The formula for calculating Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (in %)
- \( T \) = Time (in years)

3. **Set Up the Equation**: Since we want the amount to double, we know:
\[ \text{Amount} = P + SI = 2P \]
Therefore, we can express the Simple Interest as:
\[ SI = 2P - P = P \]

4. **Substitute SI in the Formula**: Now, we can substitute \( SI \) in the Simple Interest formula:
\[ P = \frac{P \times R \times T}{100} \]

5. **Cancel P from Both Sides**: Since \( P \) is common on both sides, we can cancel it out (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times T}{100} \]

6. **Rearranging the Equation**: Rearranging gives us:
\[ T = \frac{100}{R} \]

7. **Substitute the Rate**: We know \( R = 20\% \):
\[ T = \frac{100}{20} = 5 \]

8. **Conclusion**: Therefore, the time taken for the amount to double at a rate of 20% is **5 years**.

### Final Answer:
The correct answer is **(D) 5 years**.