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 16. The people who like only milk and tea together is 30% more than the people who like only coffee and milk together. People who like only coffee and milk together 20, which is double than the people who like only tea.

Find the number of people who like only one beverage.

To find the number of people who like only one beverage, let us break down the information step-by-step using a Venn diagram representation with three categories: Tea (T), Coffee (C), and Milk (M).

Let the total number of people be:
Total = 100

Let the number of people who like only Tea be denoted as $a$, only Coffee as $b$, and only Milk as $c$.
Let the number of people who like only Tea and Coffee (but not Milk) be $x_{\mathrm{tc}}$.
Let the number of people who like only Tea and Milk (but not Coffee) be $x_{\mathrm{tm}}$.
Let the number of people who like only Coffee and Milk (but not Tea) be $x_{\mathrm{cm}}$.
Let the number of people who like all three beverages be $g$.

From the given data, we can identify these values and relationships:

1. The number of people who like all three beverages is 16:
$g=16$

2. The number of people who like only Coffee and Milk together is 20:
$x_{\mathrm{cm}}=20$

3. The number of people who like only Coffee and Milk together (20) is double the number of people who like only Tea:
$x_{\mathrm{cm}}=2·a$
$20=2·a$
$a=10$
So, the number of people who like only Tea is 10.

4. The ratio of people who like only Tea and only Coffee is 5:3:
$a:b=5:3$
Since $a=10$, we have:
$\frac{10}{b}=\frac{5}{3}$
$5b=30$
$b=6$
So, the number of people who like only Coffee is 6.

5. The number of people who like only Milk and Tea together is 30% more than those who like only Coffee and Milk together:
$x_{\mathrm{tm}}=x_{\mathrm{cm}}+30\%\text{of}{x}_{\mathrm{cm}}$
$x_{\mathrm{tm}}=20·1.3=26$

6. The number of people who like only Milk is equal to the number of people who like only Tea and Coffee together:
$c=x_{\mathrm{tc}}$

Now, the sum of all categories in the Venn diagram must equal the total number of people (100):
$a+b+c+x_{\mathrm{tc}}+x_{\mathrm{tm}}+x_{\mathrm{cm}}+g=100$

Substitute the values we have found so far:
$10+6+c+x_{\mathrm{tc}}+26+20+16=100$
$78+c+x_{\mathrm{tc}}=100$
$c+x_{\mathrm{tc}}=22$

Since $c=x_{\mathrm{tc}}$, we can write:
$c+c=22$
$2c=22$
$c=11$
So, the number of people who like only Milk is 11.

Finally, we want to find the number of people who like only one beverage:
$\text{People liking only one beverage}=a+b+c$
$\text{People liking only one beverage}=10+6+11=27$

Thus, the number of people who like only one beverage is 27.