Question

In a survey of 80 people, 35 like tea, 40 like coffee and 15 like both. The number of people who like tea only, is

• A. 20
• B. 25
• C. 15
• D. 10

Hint:

In Venn diagram problems, subtract overlap to get “only” values.

Answer 1

The Correct Option is A

To solve the problem, let's use the concept of set theory. We need to determine the number of people who like tea only. Here are the steps involved:

1. Let the total number of people be represented by \(n(U) = 80\).
2. Let \(n(T)\) represent the number of people who like tea, which is given as \(35\).
3. Let \(n(C)\) represent the number of people who like coffee, which is given as \(40\).
4. Let \(n(T \cap C)\) be the number of people who like both tea and coffee, given as \(15\).
5. The number of people who like tea only can be found by subtracting the number of people who like both tea and coffee from the number of people who like tea.
6. Therefore, the formula to calculate the number of people who like tea only is:
   • \(n(T \text{ only}) = n(T) - n(T \cap C)\)
7. Substitute the given values into the formula:
   • \(n(T \text{ only}) = 35 - 15 = 20\)

Thus, the number of people who like tea only is 20. Therefore, the correct answer is

20
 

.