Consider the following statements. If a money is loaned at simple interest then the
money gets doubled in 5 years if the rate of interest is `16(2)/3%`
money gets doubled in 5 years if the rate of interest is `20%`
money becomes four times in 10 years if it gets doubled in 5 years of these statements :.

Options

A. a)(ii) and (iii) are correct
B. b)(iii) alone is correct
C. c)(ii) alone is correct
D. d)(ii) and (iii) are correct

Answer

To solve the problem, we need to analyze each of the three statements regarding simple interest and determine their validity.

### Step-by-Step Solution:

1. **Understanding Simple Interest**:
Simple Interest (SI) is calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

2. **Analyzing the First Statement**:
- Statement: "Money gets doubled in 5 years if the rate of interest is \( 16\frac{2}{3}\% \)".
- If the principal amount \( P = 100 \), then the amount after 5 years should be \( 200 \).
- The simple interest earned in this case is:
\[ SI = 200 - 100 = 100 \]
- Using the SI formula:
\[ 100 = \frac{100 \times R \times 5}{100} \]
Simplifying gives:
\[ R \times 5 = 100 \implies R = 20\% \]
- Since \( 16\frac{2}{3}\% \) is equal to \( 16.67\% \) which is less than \( 20\% \), this statement is **incorrect**.

3. **Analyzing the Second Statement**:
- Statement: "Money gets doubled in 5 years if the rate of interest is \( 20\% \)".
- Using the same principal amount \( P = 100 \):
- The simple interest earned in 5 years at \( 20\% \) is:
\[ SI = \frac{100 \times 20 \times 5}{100} = 100 \]
- Therefore, the total amount after 5 years is:
\[ 100 + 100 = 200 \]
- This statement is **correct**.

4. **Analyzing the Third Statement**:
- Statement: "Money becomes four times in 10 years if it gets doubled in 5 years".
- If the money doubles in 5 years, then after another 5 years (total 10 years), it will again earn the same interest of \( 100 \) (as calculated before).
- Therefore, the total amount after 10 years is:
\[ 200 + 100 = 300 \]
- Thus, the money does not become four times (which would be \( 400 \)), this statement is **incorrect**.

### Conclusion:
- The first statement is incorrect.
- The second statement is correct.
- The third statement is incorrect.

Thus, the only correct statement is the second one.