In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

Let $C$ denote the set of people who like coffee, and $T$ denote the set of people who like tea

$n(C \cup T)=70, n(C)=37, n(T)=52$

We know that:

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

$\therefore 70=37+52-n(C \cap T)$

$\Rightarrow 70=89-n(C \cap T)$

$\Rightarrow(C \cap T)=89-70=19$

Thus, $19$ people like both coffee and tea.

Similar Questions

Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball. Of the total, $64$ played both basketball and hockey; $80$ played cricket and basketball and $40$ played cricket and hockey; $24$ played all the three games. The number of boys who did not play any game is

In a class of $55$ students, the number of students studying different subjects are $23$ in Mathematics, $24$ in Physics, $19$ in Chemistry, $12$ in Mathematics and Physics, $9$ in Mathematics and Chemistry, $7$ in Physics and Chemistry and $4$ in all the three subjects. The total numbers of students who have taken exactly one subject is

$20$ teachers of a school either teach mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then the number of teachers teaching physics is

In a class of $140$ students numbered $1$ to $140$, all even numbered students opted Mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is

  • [JEE MAIN 2019]

In a group of $65$ people, $40$ like cricket, $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?