Question:medium

A tree grows at the rate of 1/5th of its height annually. By how much height will it grow after 2 years, if its present height is 75 cm?

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Repeated percentage growth compounds: value after $n$ years at rate $r%$ equals initial $\times\,(1+\tfrac{r}{100})^n$.
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

Step 1: Write the growth as a fraction.
Growing by 1/5th of the current height each year means the height is multiplied by \( 1 + \frac{1}{5} = \frac{6}{5} \) every year.

Step 2: Apply the fraction for two years.
After 2 years, the height is multiplied by \( \left(\frac{6}{5}\right)^2 = \frac{36}{25} \), since the growth compounds year on year.

Step 3: Substitute the starting height.
Final height \( = 75 \times \frac{36}{25} \). Since \( 75 \div 25 = 3 \), this becomes \( 3 \times 36 = 108 \) cm.

Step 4: State the final height.
The tree's height after 2 years is 108 cm.
\[ \boxed{108 \, \text{cm}} \]
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Approach Solution -2

Since the tree's growth rate of 1/5th, or 20%, per year is fixed by the question, another way to check the options is to work out what annual growth rate each one would imply over two years, and see which one equals exactly 20%.

  1. 108 cms: Going from 75 cm to 108 cm over two compounding years means the yearly multiplying factor \( x \) satisfies \( 75x^2 = 108 \), so \( x^2 = 1.44 \) and \( x = 1.2 \), which is exactly a 20% annual growth rate, matching the rate given in the question.
  2. 90 cms: Here \( x^2 = 1.2 \), giving \( x \approx 1.095 \), an implied annual growth rate of only about 9.5%, well short of the 20% stated.
  3. 144 cms: Here \( x^2 = 1.92 \), giving \( x \approx 1.386 \), an implied rate of roughly 38.6% per year, far higher than the 20% given.
  4. 112 cms: Here \( x^2 \approx 1.493 \), giving \( x \approx 1.222 \), an implied rate of about 22.2%, close to but not exactly the stated 20%.

Only the 108 cm option implies a clean, exact 20% annual growth rate, matching the rate given in the question.

So the correct answer is 108 cms.

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