The correct option is 48.

Let's break down the solution step-by-step to understand how we arrive at this answer:

Step 1: Identify the total number of cyclists.
From the given table, under the column Cycle, we can see that the total number of people who travel to work by cycle (cyclists) is:
$$\mathrm{Total\; Cyclists}=72$$

Step 2: Understand the behavior of cyclists on rainy days.
Note (b) states: "1 in 3 of the Cyclists stated that they travelled to work by bus on rainy days."
This means that on a rainy day, 1/3 of the total cyclists switch to traveling by bus, and therefore, they do not cycle.

Step 3: Calculate the number of cyclists who travel by bus on rainy days.
We find 1/3 of the 72 cyclists:
$$\mathrm{Cyclists\; switching\; to\; bus}=\frac{1}{3}\times 72=24$$

Step 4: Calculate how many people cycled to work on a rainy day.
The remaining cyclists are the ones who continue to cycle to work even on rainy days. We find this by subtracting the number of cyclists who switch to the bus from the total number of cyclists:
$$\mathrm{People\; who\; cycled\; on\; a\; rainy\; day}=\mathrm{Total\; Cyclists}-\mathrm{Cyclists\; switching\; to\; bus}$$
$$\mathrm{People\; who\; cycled\; on\; a\; rainy\; day}=72-24=48$$

Thus, 48 people cycled to work on a rainy day.