Raju's factory kept increasing its output by the same percentage every year. Find the percentage if it is known that his output is doubled after two years.
(a)$100 \sqrt{2} \%$
(b)$100(\sqrt{2}+1) \%$
(c)$100(\sqrt{2}-1) \%$
(d)$50(\sqrt{3}-1) \%$
Answer
Answer (as printed): C
Explanation
Let the initial output be $x$ and let the rate of increase be R\% per year. Then, $x\left(1+\frac{\mathrm{R}}{100}\right)^{2}=2 x \Rightarrow\left(1+\frac{\mathrm{R}}{100}\right)^{2}=2=(\sqrt{2})^{2}$ $$\Rightarrow \quad\left(1+\frac{R}{100}\right)=\sqrt{2} \Rightarrow R=100(\sqrt{2}-1) .$$
Explanation as extracted from the printed page; notation may be imperfect.