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A tree increases annually by $ \dfrac{1}{8} $ th of its height, by how much will it increase after $ 2 $ years, if it stands today $ 64 $ cm high?
A. $ 72 $ cm
B. $ 74 $ cm
C. $ 75 $ cm
D. $ 81 $ cm

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Last updated date: 22nd Jul 2024
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Answer
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Hint: Here we will first assume the unknown height of the tree be “x” and then will find the increasing of its height in two years with respect to its today’s height. Here, will frame the equation with the given fraction of the increase in height of the tree.

Complete step-by-step answer:
Given that: the initial height of the tree $ = 64 $ cm
Also, given that the tree increases every year with $ \dfrac{1}{8} $ of its initial last year’s height
Height of the tree after first year $ = $ initial height $ + \dfrac{1}{8} $ of its initial height
Height of the tree after first year $ = 64 + \dfrac{1}{8}(64) $
Simplify the above expression considering that common factors from the numerator and the denominator cancels each other.
Height of the tree after first year $ = 64 + 8 $
Height of the tree after first year $ = 72 $ cm
Now, similarly for the second year -
Height of the tree after second year $ = $ height of the tree after first year $ + \dfrac{1}{8} $ of its first year’s height
Height of the tree after second year $ = 72 + \dfrac{1}{8}(72) $
Simplify the above expression considering that common factors from the numerator and the denominator cancels each other.
Height of the tree after second year $ = 72 + 9 $
Height of the tree after second year $ = 81 $ cm
From the given multiple choices – the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Always frame the correct mathematical expression and remember every time when new height is achieved by the tree, you have to take the fraction given with the new height and add with the previous year’s height and simplify. Be good in solving the fractions and getting the values by removing the common multiples from the numerator and the denominator.