In a class of 120, 43 students will drink tea,81 students will drink coffee and 12 students will not drink both coffee and tree. how many will drink both coffee and tea?

In a class of 120, 43 students will drink tea,81 students will drink coffee and 12 students will not drink both coffee and tree. how many will drink both coffee and tea? The Correct answer is 16 students

In a class of 120, 43 students will drink tea,81 students will drink coffee and 12 students will not drink both coffee and tree. how many will drink both coffee and tea?

The Correct answer is 16 students

In a class of 120 students, we have the following information:

• Students who drink tea: 43
• Students who drink coffee: 81
• Students who do not drink both coffee and tea: 12

To find out how many students will drink both coffee and tea, we can use the principle of inclusion-exclusion. Let’s denote:

• (A): The set of students who drink tea.
• (B): The set of students who drink coffee.

We are given the following information:

• (|A|): The number of students who drink tea (43).
• (|B|): The number of students who drink coffee (81).
• (|A cup B|): The total number of students in the class (120).
• (|A cap B|): The number of students who drink both tea and coffee (what we need to find).

According to the principle of inclusion-exclusion:

[ |A cup B| = |A| + |B| - |A cap B| ]

First, let’s remove the number of students who don’t drink both tea and coffee:

Total number of students who drink tea or coffee = 120 - 12 = 108

Now, let’s solve for (|A cap B|) (the number of students who drink both tea and coffee):

[ |A cap B| = |A| + |B| - |A cup B| ] [ |A cap B| = 43 + 81 - 108 ] [ |A cap B| = 16 ]

Therefore, 16 students will drink both coffee and tea.