Question

A factory kept increasing its output by the same percentage every year .Find the percentage if it is known that the output is doubled in the last two years.

Answer 1

Let r be the increase in the rate percent per annum
Let x be the principal
According to the given information
$x{(1+\frac{r}{100})}^2=2x\Rightarrow {(1+\frac{r}{100})}^2=2\Rightarrow 1+\frac{r}{100}=\sqrt{2}\Rightarrow \frac{r}{100}=\sqrt{2}-1=1.4142-1=0.4142\Rightarrow r=0.4142\times 100=41.42\%$
Thus, the approximate increases in the rate percent is 41.42%