Question

A tree increases annually by one-fourth of its height. What will be it's height after $2$ years, if it stands $64$ cm high today?

• A. $76$ cm
• B. $80$ cm
• C. $100$ cm
• D. $105$ cm

Answer 1

The correct option is C $100$ cm

Initial height $=64cm$

Every year it increases one-fourth of it's height.

Increase $\%=(\frac{1}{4}\times 100\%)=25\%$

Height after $2$ years $=64\times {(1+\frac{25}{100})}^{2}cm$

$=64\times {(1+\frac{1}{4})}^{2}cm$

$=64\times {\left(\frac{5}{4}\right)}^{2}cm$
$=(64\times \frac{5}{4}\times \frac{5}{4})cm$
$=100cm$

Hence, the height of the tree after $2$ years will be $100cm$