Question : What will be the ratio of the interests earned by identical sum of money invested at the same rate of simple interest for 6 years and for 15 years respectively?
Option 1: 3 : 5
Option 2: 5 : 3
Option 3: 5 : 2
Option 4: 2 : 5
Correct Answer: 2 : 5
Solution :
Use the formula below.
Simple Interest = $\frac{\text{Principle×Rate×Time}}{100}$
The simple interest earned for 6 years ($SI_1$) is given by:
⇒ $SI_1$
= $\frac{P×R×6}{100}$ where $P$ and $R$ are the principal and rate of interest respectively.
Simple interest earned for 15 years ($SI_2$) is given by:
⇒ $SI_2$ = $\frac{P×R×15}{100}$
So, $\frac{SI_1}{SI_2} = \frac{ \frac{P×R×6}{100}}{\frac{P×R×15}{100}}$ = $\frac{6}{15}$ = $\frac{2}{5}$
Hence, the correct answer is 2 : 5.
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