In a company `55%` of workers drink tea,`45%` drink coffee and `40% ` drink. Milk `20%` of workers drink tea and milk both, `20%` drink coffee and milk both,` 25%` of workers tea and coffee both. `15%` of workers drink all three beverages. Find the percentage of workers who do not like any of three beverages

Answer

To solve the problem, we will use the principle of inclusion-exclusion to find the percentage of workers who do not drink any of the three beverages (tea, coffee, or milk).

### Step-by-Step Solution:

1. **Define the Variables:**
- Let \( T \) be the percentage of workers who drink tea = 55%
- Let \( C \) be the percentage of workers who drink coffee = 45%
- Let \( M \) be the percentage of workers who drink milk = 40%
- Let \( T \cap M \) be the percentage of workers who drink both tea and milk = 20%
- Let \( C \cap M \) be the percentage of workers who drink both coffee and milk = 20%
- Let \( T \cap C \) be the percentage of workers who drink both tea and coffee = 25%
- Let \( T \cap C \cap M \) be the percentage of workers who drink all three beverages = 15%

2. **Use Inclusion-Exclusion Principle:**
To find the total percentage of workers who drink at least one of the beverages, we can use the formula:
\[ P(T \cup C \cup M) = P(T) + P(C) + P(M) - P(T \cap C) - P(T \cap M) - P(C \cap M) + P(T \cap C \cap M) \]
Plugging in the values:
\[ P(T \cup C \cup M) = 55 + 45 + 40 - 25 - 20 - 20 + 15 \]

3. **Calculate the Total:**
\[ P(T \cup C \cup M) = 55 + 45 + 40 - 25 - 20 - 20 + 15 \]
\[ = 140 - 65 + 15 \]
\[ = 140 - 50 = 90 \]

4. **Find the Percentage of Workers Who Do Not Drink Any Beverage:**
The total percentage of workers who do not drink any of the three beverages is:
\[ 100\% - P(T \cup C \cup M) = 100\% - 90\% = 10\% \]

### Final Answer:
The percentage of workers who do not like any of the three beverages is **10%**.