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?
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?
Let $C$ denote the set of people who like cricket, and $T$ denote the set of people who like tennis
$\therefore n(C \cup T)=65, n(C)=40, n(C \cap T)=10$
We know that:
$n(C \cup T)=n(C)+n(T)-n(C \cap T)$
$\therefore 65=40+n(T)-10$
$\Rightarrow 65=30+n(T)$
$\Rightarrow n(T)=65-30=35$
Therefore, $35$ people like tennis.
Now,
$(T-C) \cup(T \cap C)=T$
Also.
$(T-C) \cap(T \cap C)=\varnothing$
$\therefore n(T)=n(T-C)+n(T \cap C)$
$\Rightarrow 35=n(T-C)+10 $
$\Rightarrow n(T-C)=35-10=25$
Thus, $25$ people like only tennis.
Similar Questions
In a certain school, $74 \%$ students like cricket, $76 \%$ students like football and $82 \%$ like tennis. Then, all the three sports are liked by at least $......\%$
In a certain school, $74 \%$ students like cricket, $76 \%$ students like football and $82 \%$ like tennis. Then, all the three sports are liked by at least $......\%$
- [KVPY 2009]
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
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 $140$ 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
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 city $20$ percent of the population travels by car, $50$ percent travels by bus and $10$ percent travels by both car and bus. Then persons travelling by car or bus is......$\%$
In a city $20$ percent of the population travels by car, $50$ percent travels by bus and $10$ percent travels by both car and bus. Then persons travelling by car or bus is......$\%$
In a group of students, $100$ students know Hindi, $50$ know English and $25$ know both. Each of the students knows either Hindi or English. How many students are there in the group?
In a group of students, $100$ students know Hindi, $50$ know English and $25$ know both. Each of the students knows either Hindi or English. How many students are there in the group?