A tree increases annually by `(1)/(8)` th of its height. By how much will it increase after 2 years, if it stands today 64 cm high?

Options

A. 72 cm
B. 74 cm
C. 75 cm
D. 81 cm

Answer

To solve the problem, we need to determine how much a tree that is currently 64 cm tall will increase in height over a period of 2 years, given that it grows by \( \frac{1}{8} \) of its height each year.

### Step-by-Step Solution:

1. **Identify Initial Height**:
The current height of the tree is given as 64 cm.

2. **Calculate Height After 1 Year**:
- The tree increases by \( \frac{1}{8} \) of its height annually.
- Increase after 1 year = \( \frac{1}{8} \times 64 \)
- \( \frac{1}{8} \times 64 = 8 \) cm.
- Therefore, the height after 1 year = Initial height + Increase
- Height after 1 year = \( 64 + 8 = 72 \) cm.

3. **Calculate Height After 2 Years**:
- Now, we take the height after 1 year (72 cm) and calculate the increase for the second year.
- Increase after 2 years = \( \frac{1}{8} \times 72 \)
- \( \frac{1}{8} \times 72 = 9 \) cm.
- Therefore, the height after 2 years = Height after 1 year + Increase
- Height after 2 years = \( 72 + 9 = 81 \) cm.

4. **Calculate Total Increase in Height**:
- The total increase in height over the 2 years = Height after 2 years - Initial height
- Total increase = \( 81 - 64 = 17 \) cm.

### Final Answer:
The tree will increase by **17 cm** after 2 years.