Question

In a school hostel there are 100 students out of which 60 drink tea. 50 drink coffee and 30 drink both tea and coffee. Find the number of students who do not take tea or coffee.

Answer 1

Let A and B denote the students who drink tea and coffee, respectively.
Given: n(A) = 60, n(B) = 50 and n$\left(\mathrm{A}\cap \mathrm{B}\right)$ = 30

Now, n$\left(\mathrm{A}\cup \mathrm{B}\right)$ = n(A) + n(B) $-$ n$\left(\mathrm{A}\cap \mathrm{B}\right)$
= 60 + 50 $-$ 30
= 80
It is given that the total number of students is 100.

∴ Number of students who do not like both tea and coffee = Total no. of students $-$n$\left(\mathrm{A}\cup \mathrm{B}\right)$
= 100 $-$ 80 = 20