The height of a tree increases every year `1//8` times. If the present height of the tree is 64cm, then what will be its height after 2 yr?

Options

A. 76 cm
B. 80cm
C. 81cm
D. 84cm

Answer

To solve the problem step-by-step, we need to calculate the height of the tree after 2 years given that its height increases by \( \frac{1}{8} \) times each year.

### Step 1: Understand the increase in height
The tree's height increases by \( \frac{1}{8} \) of its current height each year. This means that if the current height is \( H \), the increase in height is \( \frac{H}{8} \).

### Step 2: Calculate the new height after the first year
The present height of the tree is 64 cm. After the first year, the height will be:
\[ \text{Height after 1 year} = \text{Current height} + \text{Increase} \]
\[ = 64 + \frac{64}{8} \]
Calculating the increase:
\[ \frac{64}{8} = 8 \]
So,
\[ \text{Height after 1 year} = 64 + 8 = 72 \text{ cm} \]

### Step 3: Calculate the new height after the second year
Now, we will use the new height (72 cm) to calculate the height after the second year:
\[ \text{Height after 2 years} = \text{Height after 1 year} + \text{Increase} \]
\[ = 72 + \frac{72}{8} \]
Calculating the increase:
\[ \frac{72}{8} = 9 \]
So,
\[ \text{Height after 2 years} = 72 + 9 = 81 \text{ cm} \]

### Final Answer
The height of the tree after 2 years will be **81 cm**.

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