To solve this question, the user needs to use algebraic equations to represent the given information and solve for the number of chickens.

Let's denote the number of chickens as "c" and the number of cows as "x." We know that the total number of animals is 30, so:

c + x = 30

We also know that the total number of legs is 74. Since each chicken has 2 legs and each cow has 4 legs, we can represent the total number of legs as:

2c + 4x = 74

Now we have two equations with two variables. We can use substitution or elimination to solve for "c."

Using substitution, we can solve for "x" in the first equation and substitute it into the second equation:

x = 30 - c

2c + 4(30 - c) = 74

Simplifying the equation, we get:

-2c + 120 = 74

-2c = -46

c = 23

Therefore, the farmer has 23 chickens.

Now let's go through each option and explain why it is right or wrong:

A. 23: This option is correct. As we just showed, the farmer has 23 chickens.

B. 24: This option is incorrect. The number of chickens is 23, not 24.

C. 21: This option is incorrect. The number of chickens is 23, not 21.

D. 20: This option is incorrect. The number of chickens is 23, not 20.

The Answer is: A. 23