In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange

Hindi

1.Set Theory

easy

In a survey of $400$ students in a school, $100$ were listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

$225$

Solution

Let $U$ denote the set of surveyed students and $A$ denote the set of students taking apple juice and $B$ denote the set of students taking orange juice. Then

$n(U) = 400,n(A) = 100,n(B) = 150$ and $n(A \cap B) = 75$

Now $n\left( {{A^\prime } \cap {B^\prime }} \right) = n{(A \cup B)^\prime }$

${ = n(U) – n(A \cup B)}$

${ = n(U) – n(A) – n(B) + n(A \cap B)}$

${ = 400 – 100 – 150 + 75 = 225\,}$

Hence $225$ students were taking neither apple juice nor orange juice.

Standard 11

Mathematics

There are $200$ individuals with a skin disorder, $120$ had been exposed to the chemical $C _{1}, 50$ to chemical $C _{2},$ and $30$ to both the chemicals $C _{1}$ and $C _{2} .$ Find the number of individuals exposed to

Chemical $C _{1}$ but not chemical $C _{2}$

medium

Of the members of three athletic teams in a school $21$ are in the cricket team, $26$ are in the hockey team and $29$ are in the football team. Among them, $14$ play hockey and cricket, $15$ play hockey and football, and $12$ play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is

medium

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.

medium

Two newspaper $A$ and $B$ are published in a city. It is known that $25\%$ of the city populations reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ and $B$. Further, $30\%$ of those who read $A$ but not $B$ look into advertisements and $40\%$ of those who read $B$ but not $A$ also look into advertisements, while $50\%$ of those who read both $A$and $B$ look into advertisements. Then the percentage of the population who look into advertisement is

hard

(JEE MAIN-2019)

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?

medium