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......$\%$

- A
$80$

- B
$40$

- C
$60$

- D
$70$

In a survey of $220$ students of a higher secondary school, it was found that at least $125$ and at most $130$ students studied Mathematics; at least $85$ and at most $95$ studied Physics; at least $75$ and at most $90$ studied Chemistry; $30$ studied both Physics and Chemistry; $50$ studied both Chemistry and Mathematics; $40$ studied both Mathematics and Physics and $10$ studied none of these subjects. Let $\mathrm{m}$ and $\mathrm{n}$ respectively be the least and the most number of students who studied all the three subjects. Then $\mathrm{m}+\mathrm{n}$ is equal to .............................

- [JEE MAIN 2024]

An organization awarded $48$ medals in event '$A$',$25$ in event '$B$ ' and $18$ in event ' $C$ '. If these medals went to total $60$ men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

- [JEE MAIN 2023]

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 $1,3$ read all three newspapers. Find:

the number of people who read exactly one newspaper.

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?

- [KVPY 2017]

In a class of $35$ students, $24$ like to play cricket and $16$ like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?