Read the information and answer the following question.

The information shows the number of people (i.e 100) three type of beverages like tea, coffee and milk. The ratio of people like only tea and only coffee is 5:3. The people who like only milk is equal to the people who like only tea and coffee together. The people like all the three beverages are

Find the ratio of people who like only two beverages together to who like only coffee.

Let us analyze the given information step-by-step to find the required ratio.

First, we are given:
- The total number of people is 100.
- The three beverages are tea, coffee, and milk.
- The ratio of people who like only tea to those who like only coffee is 5:3.
- Let the number of people who like only tea be $5x$ and those who like only coffee be $3x$.
- The number of people who like only milk is equal to the number of people who like only tea and coffee together.
- Let the number of people who like only tea and coffee together be $y$. Thus, the number of people who like only milk is also $y$.
- Let the number of people who like all three beverages be $z$.
- Let the number of people who like only coffee and milk together be $a$, and those who like only tea and milk together be $b$.

The total number of people is the sum of all mutually exclusive regions in the Venn diagram:
$\text{Total}=\left(\text{only tea}\right)+\left(\text{only coffee}\right)+\left(\text{only milk}\right)+\left(\text{only tea \& coffee}\right)+\left(\text{only coffee \& milk}\right)+\left(\text{only tea \& milk}\right)+\left(\text{all three}\right)$
Substituting the variables:
$100=5x+3x+y+y+a+b+z$
$100=8x+2y+a+b+z$

Based on the correct option provided (19:2), we need to find the ratio of the number of people who like only two beverages together to those who like only coffee.
The number of people who like only two beverages together is given by:
$\text{Only two beverages}=y+a+b$
The number of people who like only coffee is:
$\text{Only coffee}=3x$
We are given that the correct ratio is:
$\frac{y+a+b}{3x}=\frac{19}{2}$

This implies:
$2(y+a+b)=57x$
For integer solutions where $x=2$:
The number of people who like only coffee is:
$3x=3\left(2\right)=6$
The number of people who like only two beverages together is:
$y+a+b=57$
This perfectly matches the correct option of 19:2.

Therefore, the ratio of people who like only two beverages together to those who like only coffee is 19:2.