Question:medium

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

Step 1: Find the growth after year 1.
The tree grows by \( \frac{1}{5} \) of its current height each year. Starting height is 75 cm. Growth in year 1 \( = \frac{1}{5} \times 75 = 15 \) cm. Height after year 1 \( = 75 + 15 = 90 \) cm.

Step 2: Find the growth after year 2.
Growth in year 2 is \( \frac{1}{5} \) of the height at the start of year 2, which is now 90 cm. Growth in year 2 \( = \frac{1}{5} \times 90 = 18 \) cm.

Step 3: Add up the final height.
Height after 2 years \( = 90 + 18 = 108 \) cm.

Step 4: Final Answer.
Since growth compounds on the previous year's height, the tree reaches 108 cm after 2 years. \[ \boxed{108 \text{ cm}} \]
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Approach Solution -2

A growth of 1/5th of the current height each year is the same as a 20% annual growth rate, and the combined effect of two successive 20% increases can be found using the percentage-change formula \( a+b+\frac{ab}{100} \) rather than adding the growth in two separate steps.

  1. 108 cms: With \( a=20 \) and \( b=20 \), the combined percentage increase is \( 20+20+\frac{20\times20}{100}=40+4=44\% \). Applying a 44% increase to 75 cm gives \( 75 \times 1.44 = 108 \) cm, matching this option.
  2. 90 cms: This corresponds to only a 20% increase over one year, not the 44% combined increase over two years that the formula gives.
  3. 144 cms: This would need a combined growth rate far higher than the 44% that two successive 20% increases actually produce.
  4. 112 cms: Applying a 44% increase to 75 cm does not land on this figure, so it is inconsistent with the calculated compound rate.

Using the successive percentage change formula shows the two years of 20% growth combine to a 44% overall increase, taking the tree from 75 cm to exactly 108 cm.

Therefore, the correct answer is 108 cms.

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