In a group of students, $100$ students know Hindi, $50$ know English and $25$ know both. Each of the students knows either Hindi or English. How many students are there in the group?
Let $U$ be the set of all students in the group.
Let $E$ be the set of all students who know English.
Let $H$ be the set of all students who know Hindi.
$\therefore H \cup E=U$
Accordingly, $n(H)=100$ and $n(E)=50$
$n(H \cap E)=25$
$n(U)=n(H)+n(E)-n(H \cap E)$
$=100+50-25$
$=125$
Hence, there are $125$ students in the group.
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?
In a town of $10,000$ families it was found that $40\%$ family buy newspaper $A, 20\%$ buy newspaper $B$ and $10\%$ families buy newspaper $C, 5\%$ families buy $A$ and $B, 3\%$ buy $B$ and $C$ and $4\%$ buy $A$ and $C$. If $2\%$ families buy all the three newspapers, then number of families which buy $A$ only is
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 $C_{1}$ or chemical $C_{2}$
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
In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?