1. The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23 : 7 respectively. What is rate of interest per annum (in %)?
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By: anil on 05 May 2019 01.48 am
Let rate of interest = $$r\%$$ Difference between compound interest and simple interest on Rs. $$P$$ for 2 years = $$P(frac{r}{100})^2$$
Difference for 3 years = $$P(frac{r}{100})^2(frac{r}{100}+3)$$ According to ques, => $$P(frac{r}{100})^2(frac{r}{100}+3):P(frac{r}{100})^2=23:7$$ => $$frac{(frac{r}{100}+3)}{1}=frac{23}{7}$$ => $$7(frac{r}{100}+3)=23$$ => $$frac{7r}{100}+21=23$$ => $$frac{7r}{100}=23-21=2$$ => $$r=frac{100}{7} imes2=frac{200}{7}\%$$ => Ans - (A)
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Difference for 3 years = $$P(frac{r}{100})^2(frac{r}{100}+3)$$ According to ques, => $$P(frac{r}{100})^2(frac{r}{100}+3):P(frac{r}{100})^2=23:7$$ => $$frac{(frac{r}{100}+3)}{1}=frac{23}{7}$$ => $$7(frac{r}{100}+3)=23$$ => $$frac{7r}{100}+21=23$$ => $$frac{7r}{100}=23-21=2$$ => $$r=frac{100}{7} imes2=frac{200}{7}\%$$ => Ans - (A)