Question

Out of 260 students in a class of a school, 135 like tea, 110 like coffee and 80 like milk, 35 of these like both tea and coffee, 30 like both tea and milk, 20 like both coffee and milk. Also, each student likes atleast one of the three drinks. How many students like all the three drinks?

• A. 30
• B. 15
• C. 20
• D. 25

Answer 1

The correct option is C 20

Let T, C and M be the sets of students who like tea, coffee and milk respectively. Let x number of students like all the three drinks.
It is given that the number of students who like both tea and coffee is 35. So, number of students who like only tea and coffee is (35-x).
Similarly, the number of students who like various drinks are written in the regions representing them in the venn diagram.
It is given that each student likes atleast one of the drinks.
$\because n(T\cup C\cup M)=260,$ we have
$(70+x)+(55+x)+(30+x)+(35-x)+(30-x)+(20-x)+x=260.$
$\Rightarrow 240+x=260$
$\Rightarrow x=20$
Hence, 20 students like all the three drinks.