Average hourly earnings per year (E) of the workers in a firm are represented in figures A and B as follows:

From the figures, it is observed that the

The correct option is: Slopes of the graphs are same.

By carefully analyzing Fig. A and Fig. B, we can observe and extract the following data points for the years ($Y$) and hourly earnings ($E$):

For Fig. A:
- In the year 2013, $E=20$
- In the year 2014, $E=25$
- In the year 2015, $E=30$
- In the year 2016, $E=35$
- In the year 2017, $E=40$

For Fig. B:
- In the year 2013, the line starts at $E=20$
- In the year 2014, the point lies midway between 20 and 30, meaning $E=25$
- In the year 2015, $E=30$
- In the year 2016, the point lies midway between 30 and 40, meaning $E=35$
- In the year 2017, $E=40$

Let us evaluate each of the given options based on these details:

1. Values of E:
The values of $E$ at each corresponding year are identical in both figures (ranging from 20 to 40). Hence, the values of $E$ are the same, not different.

2. Ranges of E:
The range is defined as the difference between the maximum and minimum values:

$$\text{Range}=E_{\text{max}}-E_{\text{min}}=40-20=20$$

Since this range is $20$ in both cases, the ranges of $E$ are the same.

3. Slopes of the graphs:
The mathematical slope of a linear graph represents the rate of increase of $E$ per year:

$$\text{Slope}=\frac{\Delta E}{\Delta Y}=\frac{40-20}{2017-2013}=\frac{20}{4}=5\text{units/year}$$

Since both graphs model the same data points, the mathematical slope (rate of increase) is exactly the same, which is $5$ dollars per year.

Note: The visual difference in the steepness of the lines is due to the different vertical scales used. Fig. A has a vertical axis starting at 20, which compresses the height and makes the rise look steeper. Fig. B has a vertical axis starting at 0, making the rise look gentler. However, mathematically, their actual slopes are identical.