1. A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years does the same amount becomes Rs. 8000.
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By: anil on 05 May 2019 01.50 am
Let the rate of interest = $$r\%$$ Principal = Rs. 2000 and time = 2 years Amount under compound interest = $$P(1+frac{r}{100})^t$$ => $$2000(1+frac{r}{100})^2=4000$$ => $$(1+frac{r}{100})^2=frac{4000}{2000}=2$$ => $$(1+frac{r}{100})=sqrt2$$ ----------(i) Let the sum amounted to Rs. 8000 in $$t$$ years => $$2000(1+frac{r}{100})^t=8000$$ Substituting value from equation (i) => $$(sqrt2)^t=frac{8000}{2000}=4$$ => $$(2)^{frac{t}{2}}=(2)^2$$ => $$frac{t}{2}=2$$ => $$t=2 imes 2=4$$ years => Ans - (B)
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