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.

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)

=> $$(\sqrt2)^t=\frac{8000}{2000}=4$$

=> $$(2)^{\frac{t}{2}}=(2)^2$$

=> $$\frac{t}{2}=2$$

=> $$t=2 \times 2=4$$ years

=> Ans - (B)