Question

In a hostel 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take both tea and coffee, 8 students take both coffee and milk. None of them take tea and milk both and everyone takes at least one beverage. Find the number of students in the hostel?

Answer 1

Hint: Use the union and intersection of sets to solve this question.
Use the relation of intersection of two sets and total no. of elements in sets

Complete step by step solution: Number of students taking tea \[=25\].
Number of students taking coffee \[=20\].
Number of students taking milk \[=15\].
Number of students took both tea and coffee \[=10\].
Number of students took both coffee and milk \[=8\].

Total number of student
\[\Rightarrow 15+10+8+2+0+7\].
\[\Rightarrow 25+10+7\]
\[\Rightarrow 42\]
Total No. Of student in hostel are 42

Note: 1. Use the application of set theory
2. There is no student to take tea and milk both, so the intersection of the set of milk and tea is 0.