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?
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?
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
An organization awarded $48$ medals in event '$A$',$25$ in event '$B$ ' and $18$ in event ' $C$ '. If these medals went to total $60$ men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
An organization awarded $48$ medals in event '$A$',$25$ in event '$B$ ' and $18$ in event ' $C$ '. If these medals went to total $60$ men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
- [JEE MAIN 2023]
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]
In a certain town, $25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements
$(A)\,\,\,5\%$ families own both a car and a phone
$(B)\,\,\,35\%$ families own either a car or a phone
$(C)\,\,\,40,000$ families live in the town
Then,
In a certain town, $25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements
$(A)\,\,\,5\%$ families own both a car and a phone
$(B)\,\,\,35\%$ families own either a car or a phone
$(C)\,\,\,40,000$ families live in the town
Then,
- [JEE MAIN 2015]
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
A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?
A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?