Consider the following statements If a sum of money is lent at simple interest, then the 1. money gets doubled in 5 years if the rate of interest is $16\\frac{2}{3}$% 2. money gets doubled in 5 years if the rate of interest is 20%. 3. money becomes four times in 10 years if it gets doubled in 5 years. Of these statements,

### Concept & Simple Interest Let's evaluate each statement individually using simple interest formulas. For a sum to double, $S.I. = P$. For a sum to become four times, $S.I. = 3P$. ### Step-by-Step Solution * **Statement 1:** Sum doubles $\Rightarrow S.I. = P$. Time = 5 years. Rate $= \frac{100 \times S.I.}{P \times T} = \frac{100 \times P}{P \times 5} = 20$%. Statement 1 says rate is $16\frac{2}{3}$%, so it is **False**. * **Statement 2:** Sum doubles in 5 years. As calculated above, Rate = 20%. Statement 2 says rate is 20%, so it is **True**. * **Statement 3:** Sum doubles in 5 years $\Rightarrow S.I. = P$ in 5 years. To become 4 times, $S.I. = 3P$. Time required $= 3 \times 5 = 15$ years. Statement 3 says 10 years, so it is **False**. ### Exam Strategy & Shortcut Verify each statement quickly. 1. $R = 100/5 = 20 \neq 16.66$. (False) 2. $R = 100/5 = 20$. (True) 3. If $SI = P$ in 5 yrs, then $SI = 3P$ in $3 \times 5 = 15$ yrs. (False) Only statement 2 is correct. ### Common Pitfall In statement 3, thinking that if it doubles in 5 years, it becomes 4 times in 10 years by applying compound interest logic. For simple interest, the interest grows linearly, not exponentially. ### Final Answer Therefore, the correct answer is **2 alone is correct**.