Question : After 55 years, a sum invested at simple interest at the rate of $r$ percent becomes twice of itself. What is the value of $r$?
Option 1: $\frac{17}{20}\%$
Option 2: $\frac{11}{30}\%$
Option 3: $\frac{13}{15}\%$
Option 4: $\frac{20}{11}\%$
Correct Answer: $\frac{20}{11}\%$
Solution :
Time = 55 years
Principal = $\text{P}$
Rate = $\text{r}$
Amount = $\text{2P}$
Simple interest = Amount – Principal = $\text{2P – P = P}$
We know that,
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
$⇒\text{P} = \frac{\text{P × r × 55}}{100}$
$⇒\text{r} = \frac{100}{55}= \frac{20}{11}\%$
Hence, the correct answer is $\frac{20}{11}\%$.
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