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 milk and coffee. none of them take tea and milk both and everyone takes atleast one beverage. find the number of students in the hostel. represent it with a venn diagram.

Answer 1

Students who take  Just Tea= 15  Just Coffee= 2  just milk= 7  tea and coffee= 10 milk and coffee= 8  Answer= 42 students

Answer 2

Answer:

Total number of students in the hostel is 42.                

Step-by-step explanation:

Given : 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 milk and coffee. None of them take tea and milk both and everyone takes at least one beverage.

To find : The number of students in the hostel and represent it with a Venn diagram?

Solution :

Let T- tea, C - coffee and M - milk

According to question,

n(T)=25

n(C)=20

n(M)=15

$n(T\cap C)=10$

$n(M\cap C)=8$

None of them take tea and milk both and everyone takes at least one beverage.

$n(T\cap M)=0$

$n(T\cap M\cap C)=0$

To find the number of students is given by,

$n(T\cup M\cup C)=n(T)+n(C)+n(M)-n(T\cap C)-n(M\cap C)-n(T\cap M)+n(T\cap M\cap C)$

$n(T\cup M\cup C)=25+20+15-10-8-0+0$

$n(T\cup M\cup C)=42$

Therefore, Total number of students in the hostel is 42.

Refer the attached figure below for venn diagram.