To solve this problem, we can use the concept of ratios and proportions. Let's break it down step by step:

Step 1: Understanding the given information
The ratio of two quantities is given as 3:4. This means that for every 3 units of the first quantity, there are 4 units of the second quantity.

Step 2: Finding the antecedent of the inverse ratio
The antecedent of the inverse ratio refers to the first value in the inverse ratio. In other words, it is the value that comes after the colon in the inverse ratio.

In this case, the antecedent of the inverse ratio is given as 100. This means that the inverse ratio is 100:something.

Step 3: Finding the consequent of the inverse ratio
To find the consequent of the inverse ratio, we need to determine the value that corresponds to the inverse ratio.

Since the ratio of the two quantities is 3:4, the inverse ratio is 4:3. This means that for every 4 units of the first quantity, there are 3 units of the second quantity.

Given that the antecedent of the inverse ratio is 100, we can set up the following proportion:

4/3 = 100/x

Cross-multiplying, we get:

4x = 3 * 100
4x = 300

Dividing both sides by 4, we find:

x = 300/4
x = 75

Therefore, the consequent of the inverse ratio is 75.

Step 4: Determining the correct answer
The question asks for the value of the consequent of the inverse ratio. We have found that the consequent is 75.

Among the given options (a) 75, (b) 1200, (c) 120, and (d) None of these, the correct answer is option (a) 75.

So, the correct answer is option 'A'.