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

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

medium

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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?

hard

(KVPY-2017)

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,

hard

(JEE MAIN-2015)

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……$\%$

easy

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

medium

(JEE MAIN-2020)