Question

In a college 200 students are randomly chosen. 140 like tea and 120 like Coffee and 70 like both tea and coffee.How many like neither tea nor coffee?

• A. 20
• B. 30
• C. 50
• D. 10

Answer 1

The Correct Option is D

To solve the problem of finding how many students like neither tea nor coffee, we can use the principle of set theory. Let's define the sets:

• Let \( T \) be the set of students who like tea.
• Let \( C \) be the set of students who like coffee.

The given information can be laid out as follows: 

• \(|T| = 140\), which means 140 students like tea.
• \(|C| = 120\), which means 120 students like coffee.
• \(|T \cap C| = 70\), which means 70 students like both tea and coffee.
• Total number of students, \(|U| = 200\).

Using the principle of inclusion-exclusion, we can calculate the number of students who like either tea or coffee or both:

\(|T \cup C| = |T| + |C| - |T \cap C|\)

Substituting the values:

\(|T \cup C| = 140 + 120 - 70 = 190\)

This result means that 190 students like either tea, coffee, or both.

Hence, the number of students who like neither tea nor coffee is:

\(|U| - |T \cup C| = 200 - 190 = 10\)

Thus, the number of students who like neither tea nor coffee is 10.

The correct answer is 10.