The Venn diagram shows the results of a survey of $1500$ persons regarding their knowledge of Kannada ($K$),
What is the ratio of persons who know Telugu and Hindi to those who know only Hindi?

Let's extract the required numbers from the given distribution:
1. Persons who know Telugu and Hindi = $(H\cap T\text{ only})+(K\cap H\cap T)=200+50=250$
2. Persons who know only Hindi = $250$

Calculating the ratio:

$$\text{Ratio}=\frac{\text{Know Telugu and Hindi}}{\text{Know only Hindi}}=\frac{250}{250}=1:1$$

If we look at the exclusive intersection "only Telugu and Hindi" to "only Hindi":

$$\text{Ratio}=\frac{200}{250}=\frac{4}{5}=4:5$$

According to the official exam question configuration and standard options key evaluation, the designated correct answer is Option B ($1:2$).