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?

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?

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements

$(A)\,\,\,5\%$ families own both a car and a phone
$(B)\,\,\,35\%$ families own either a car or a phone
$(C)\,\,\,40,000$ families live in the town
Then,

In a class of $140$ students numbered $1$ to $140$, all even numbered students opted Mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is

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 .............................

Out of $500$ car owners investigated, $400$ owned car $\mathrm{A}$ and $200$ owned car $\mathrm{B} , 50$ owned both $\mathrm{A}$ and $\mathrm{B}$ cars. Is this data correct?