Step 1: Identify heights from the graph

From the given bar graph, the height of Amit is $140\text{ cm}$ and the height of Rahul is $160\text{ cm}$.

$\text{Height of Amit} = 140\text{ cm}, \quad \text{Height of Rahul} = 160\text{ cm}$

Step 2: Set up the ratio

We need to find the respective ratio between the height of Amit and the height of Rahul.

$\text{Ratio} = \frac{140}{160}$

Step 3: Simplify the ratio

Dividing both numerator and denominator by their greatest common divisor, which is $20$: $\frac{140 \div 20}{160 \div 20} = \frac{7}{8}$

$7:8$