In a survey of $600$ students in a school, $150$ students were found to be taking tea and $225$ taking coffee, $100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

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

Let $U$ be the set of all students who took part in the survey.

Let $T$ be the set of students taking tea.

Let $C$ be the set of students taking coffee.

Accordingly, $n(U)=600, n(T)=150, n(C)=225, n(T \cap C)=100$

To find : Number of student taking neither tea nor coffee i.e., we have to find $n\left(T^{\prime} \cap C^{\prime}\right)$

$n\left(T^{\prime} \cap C^{\prime}\right)=n(T \cup C)^{\prime}$

$=n(U)-n(T \cup C)$

$=n(U)-[n(T)+n(C)-n(T \cap C)]$

$=600-[150+225-100]$

$=600-275$

$=325$

Hence, $325$ students were taking neither tea nor coffee.

Similar Questions

A survey shows that $63 \%$ of the people in a city read newspaper $A$ whereas $76 \%$ read newspaper $B$. If $x \%$ of the people read both the newspapers, then a possible value of $x$ can be

  • [JEE MAIN 2020]

In a survey of $60$ people, it was found that $25$ people read newspaper $H , 26$ read newspaper $T, 26$ read newspaper $I, 9$ read both $H$ and $I, 11$ read both $H$ and $T,$ $8$ read both $T$ and $1,3$ read all three newspapers. Find:

the number of people who read at least one of the newspapers.

A survey shows that $73 \%$ of the persons working in an office like coffee, whereas $65 \%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be

  • [JEE MAIN 2020]

In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2: 3$. If further $44$ girls leave the class, then class the ratio of boys to girls is $5: 2$. How many more boys should leave the class so that the number of boys equals that of girls?

  • [KVPY 2017]

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?