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?

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?

In a survey of $400$ students in a school, $100$ were listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

In a Mathematics test, the average marks of boys is $x \%$ and the average marks of girls is $y \%$ with $x \neq y$. If the average marks of all students is $z \%$, the ratio of the number of girls to the total number of students is

In a group of $400$ people, $250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

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 $C _{1}$ but not chemical $C _{2}$