Question

A boy carved his initials on the bark of a tree at a height of $2.5$m above the ground when the tree was $5$m tall. In $10$ years the tree attained a height of $15$m. The initials carved by the boy $10$ years ago will now be found.

• A. At $12.5$m above the ground
• B. At $7.5$m above the ground
• C. At $2.5$m above the ground
• D. At $15.0$m above the ground

Answer 1

The correct option is B At $7.5$m above the ground

$\begin{array}{c}\text{Intial height of tree}=5m\\ \text{Initial height of initids}=2.5m\\ \text{i.e initials carved at}\\ \text{the middle of the}\text{tree.}\end{array}$

$\begin{array}{c}\therefore \text{after l0 years, each section}\text{of tree would have been}\\ \text{grown in height, therefore}\text{the initials would still}\\ \text{be carved at the}\text{centre of the tree}\text{after l0 years.}\end{array}$

$\begin{array}{c}\text{Height of tree after}\text{l0 years}=15m\\ \text{Height of initials}\text{after l0 years}=\frac{15}{2}m=7.5m\end{array}$