Question

In a company, 35% of the employees drink coffee, 40% of the employees drink tea, and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

• A. 15
• B. 25
• C. 35
• D. 40

Hint:

Use the principle of inclusion-exclusion to calculate the union of two sets when there is an overlap (i.e., employees who drink both tea and coffee).

Answer 1

The Correct Option is C

Let the total number of employees be \( N \). The number of employees who drink coffee is 35% of \( N \), i.e., \( 0.35N \). The number of employees who drink tea is 40% of \( N \), i.e., \( 0.40N \). The number of employees who drink both coffee and tea is 10% of \( N \), i.e., \( 0.10N \). Using the principle of inclusion-exclusion to calculate the number of employees who drink either tea or coffee: \[ \text{Employees who drink tea or coffee} = (0.35N + 0.40N - 0.10N) = 0.65N \] The number of employees who drink neither tea nor coffee is the complement: \[ \text{Employees who drink neither} = N - 0.65N = 0.35N \] Thus, the percentage of employees who drink neither tea nor coffee is 35%. Therefore, the correct answer is option (C).
Final Answer: 35