Question:
A tree grows at the rate of \(\frac 15^{th}\) of its height annually. By how much height will it grow after 2 years, if its present height is 75 cms?
A tree grows at the rate of \(\frac 15^{th}\) of its height annually. By how much height will it grow after 2 years, if its present height is 75 cms?
Updated On: Jul 15, 2026
- 108 cms
- 90 cms
- 144 cms
- 112 cms
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The Correct Option is A
Approach Solution - 1
The correct option is (A): 108 cms.
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The question says a tree grows by 1/5th of its current height every year, starting from a present height of 75 cm, and asks for its height after 2 years. Since the growth compounds (each year's growth is based on the height reached so far), we can test each option by growing 75 cm forward year by year and checking which option matches.
- 108 cms: After year 1, the tree grows by \( \frac{1}{5} \) of 75 cm, which is 15 cm, taking it to 90 cm. After year 2, it grows by \( \frac{1}{5} \) of 90 cm, which is 18 cm, taking it to \( 90+18=108 \) cm. This matches exactly.
- 90 cms: This is the height after only 1 year of growth, not 2, since the tree is still growing in the second year and does not stop at 90 cm.
- 144 cms: Reaching 144 cm from 75 cm in two years would need a much faster growth rate than 1/5th per year; testing it against the given rate does not produce this figure.
- 112 cms: This value does not arise from compounding two successive 1/5th increases on 75 cm, and checking the arithmetic shows it is not consistent with the given growth rate.
Growing the height forward one year at a time, using 1/5th of the current height each year, lands exactly on 108 cm after 2 years.
Therefore, the correct answer is 108 cms.
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Approach Solution -3
The question says a tree grows by 1/5th of its current height every year, starting at 75 cm, and asks for its height after 2 years. Growing by 1/5th each year is the same as multiplying the height by \( \frac{6}{5} \) every year, so applying that multiplier twice gives the height directly without adding the growth step by step.
- 108 cms: Multiplying twice by \( \frac{6}{5} \) gives an overall factor of \( \left(\frac{6}{5}\right)^2 = \frac{36}{25} \). Applying this to the starting height, \( 75 \times \frac{36}{25} = 3 \times 36 = 108 \) cm, matching this option exactly.
- 90 cms: This equals \( 75 \times \frac{6}{5} \), the height after only a single year's growth, not the compounded two-year multiplier.
- 144 cms: Reaching this figure from 75 cm would require a combined growth factor larger than \( \frac{36}{25} \), which does not match the given annual rate of 1/5th.
- 112 cms: This value does not correspond to \( 75 \times \frac{36}{25} \) or to any two-step application of the \( \frac{6}{5} \) multiplier.
Applying the \( \frac{6}{5} \) growth multiplier twice in a row to the starting height of 75 cm produces exactly 108 cm.
Therefore, the correct answer is 108 cms.
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