In a school of $800$ boys,$224$ play cricket,$240$ play hockey,and $336$ play basketball. Of the total,$64$ play basketball and hockey,$80$ play cricket and basketball,and $40$ play cricket and hockey,while $24$ play all three games. Find the number of boys who do not play any game.

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments,then $K$ cannot belong to the set :

$A$ contractor has two teams of workers,team $A$ and team $B$. Team $A$ can complete a project $P$ in $12$ days and team $B$ can complete $P$ in $36$ days. Team $A$ starts working on $P$ and team $B$ joins team $A$ after four days. Team $A$ is withdrawn after another two days and team $B$ is asked to double its efficiency. The number of additional days required for team $B$ to complete $P$ is

If ${A_1}, {A_2}, {A_3}, \dots, {A_{30}}$ are $30$ sets each having $5$ elements and ${B_1}, {B_2}, \dots, {B_n}$ are $n$ sets each having $3$ 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:

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 $I$,and $3$ read all three newspapers. Find the number of people who read exactly one newspaper.

In a survey,it was found that $63\%$ of Americans like cheese and $76\%$ like apples. If $x\%$ of Americans like both cheese and apples,then: