Practical Problems on Union and Intersection of Two Sets

$A, B, C$ are $3$ newspapers from a city, $20\%$ of the population read $A$, $16\%$ read $B,14\%$ read $C,8\%$ both $A$ and $B,5\%$ both $A$ and $C$, $4\%$ both $B$ and $C$ and $2\%$ all the three. Find the percentage of the population who read at least one newspaper.

In a school there are $20$ teachers who teach Mathematics or Physics. Of these, $12$ teach Mathematics and $4$ teach both Physics and Mathematics. How many teachers teach Physics?

In a survey of $425$ students in a school, it was found that $115$ drink apple juice, $160$ drink orange juice and $80$ drink both apple as well as orange juice. How many drink neither apple juice nor orange juice?

In a survey, it was found that $21$ people liked the product $A$, $26$ liked the product $B$, and $29$ people liked the product $C$. If $14$ people liked the product $A$ and $B$, $12$ people liked the product $C$ and $A$,$14$ people liked the product $B$ and $C$ and $8$ people liked all the products. Find how many people like products $A$ and $C$ not $B$.

If $A, B, C$ are three sets and $U$ is the universal set such that $n\left(U\right)=700,n\left(A\right)=200, n\left(B\right)=300$ and $n(A\cap B)=100$. Find $n\left(A^{\text{'}}\cap B^{\text{'}}\right)$.

In a group of $20$ students, $12$ take tea, $16$ take coffee and $3$ take neither of the two. How many take both tea and coffee?

In a committee, $50$ people speak French, $20$ speak Spanish and $10$ speak both Spanish and French. How many people speak at least one of these two languages? 

In a college of $300$ students, every student reads$5$ newspaper and every newspaper is read by $60$ students. The total number of newspapers 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 certain town $25\%$ families own a cell phone, $15\%$ families own a scooter and $65\%$ families own neither a cell phone nor a scooter. If $1500$ families own both a cell phone and a scooter, then the total number of families in the town is

There are $600$ boys in a hostel. Each plays either hockey or football or both. If $75\%$ play hockey and $45\%$ play football, how many play both?

In an examination $34\%$ of the students failed in Mathematics and $42\%$ failed in English. If $20\%$ of the students failed in both the subjects, then the percentage of students who passed in both the subjects was:

A class has $175$students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, physics $70$chemistry $40$; mathematics and physics $30$ , mathematics and chemistry $28$, physics and chemistry $23$, mathematics, physics and chemistry $18$. How many students have offered mathematics alone?

In a certain town $25\%$ families own a phone and $15\%$ own a car, $65\%$ families own neither a phone nor a car. $2000$ families own both a car and a phone. Consider the following statements in this regard:

$1.$ $10\%$ families own both a car and a phone
$2.$ $35\%$ families own either a car or a phone
$3.$ $40,000$ families live in the town
Which of the above statements are correct

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X\mathit{\cup }Y$ has $60$ elements and $X\mathit{\cap }Y$ has $10$ elements, how many elements does $Y$ have ?