A tree increases annually by 1/8 of its height. By how much will it increase after 21/2 years if it stands today 8 m high ?

Answer: Option A

Percentage annual increase
$$\begin{array}{rl}& =\left(\frac{1}{8}\times 100\right)\%\\ & =\frac{25}{2}\%\end{array}$$
Height after $$2\frac{1}{2}$$ years
$$\begin{array}{rl}& =\left[8{\left(1+\frac{25}{2\times 100}\right)}^2\left(1+\frac{25}{4\times 100}\right)\right]m\\ & =\left(8\times \frac{9}{8}\times \frac{9}{8}\times \frac{17}{16}\right)m\\ & =\left(\frac{1377}{128}\right)m\\ & =10.75m\end{array}$$