The bar graph shows GDP for the year 2017, in billion USD, of six countries which have united to form a free trade block. GDP of which country constitutes $\frac{1}{5}$ th of the total GDP of these $6$ countries?

First, let's calculate the total GDP of all six countries combined by adding up the values from each bar:
$$\text{Total GDP}=125\text{ (A)}+100\text{ (B)}+150\text{ (C)}+200\text{ (D)}+100\text{ (E)}+75\text{ (F)}$$

$$\text{Total GDP}=125+100+150+200+100+75=750\text{ billion USD}$$

Now, find the target GDP value which is $\frac{1}{5}$ th of the total GDP:

$$\text{Target GDP}=\frac{1}{5}\times 750=150\text{ billion USD}$$

Matching this target value with the given graph, Country C has a GDP of exactly $150$ billion USD.