Correct Answer - Option 3 : 12.5%
Given:
Ratio of difference for 3 years and 2 years = 25 : 8
Formula used:
(CI – SI) for 2 years = \(\frac{{{\rm{P}}{{\left( {\rm{r}} \right)}^2}}}{{{{100}^2}}}\)
(CI – SI) for 3 years = \(\frac{{{\rm{P}}{{\left( {\rm{r}} \right)}^2}}}{{{{100}^2}}} \times \frac{{\left( {300{\rm{\;}} + {\rm{\;r}}} \right)}}{{100}}\)
Calculation:
According to the question,
\(\frac{{{\frac{{{\rm{P}}{{\left( {\rm{r}} \right)}^2}}}{{{{100}^2}}} \times \frac{{\left( {300{\rm{\;}} + {\rm{\;r}}} \right)}}{{100}}}}}{\frac{{{\rm{P}}{{\left( {\rm{r}} \right)}^2}}}{{{{100}^2}}}} = \frac{\rm25}{8}\)
⇒ \(\frac{{\left( {300{\rm{\;}} + {\rm{\;r}}} \right)}}{{100}} = \frac{25}{8}\)
⇒ 2400 + 8r = 2500
⇒ 8r = 2500 – 2400
⇒ 8r = 100
⇒ r = 100/8
⇒ Rate = 12.5%
The rate of interest is 12.5%
