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,the ratio of boys to girls becomes $5:2$. How many more boys should leave the class so that the number of boys equals that of girls?

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

$A$ 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

In a group of $65$ people,$40$ like cricket and $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

In a survey,it was found that $21$ people liked product $A$,$26$ liked product $B$,and $29$ liked product $C$. If $14$ people liked products $A$ and $B$,$12$ people liked products $C$ and $A$,$14$ people liked products $B$ and $C$,and $8$ liked all three products,find how many people liked product $C$ only.

In a city,$25\%$ of families have a telephone and $15\%$ have a car,while $65\%$ of families have neither a telephone nor a car. If $2000$ families have both a car and a telephone,then consider the following statements:
$1.$ $10\%$ of families have both a car and a telephone.
$2.$ $35\%$ of families have either a car or a telephone.
$3.$ $40,000$ families live in the city.
Which of these statements are true?