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
$\frac{z-x}{y-x}$
$\frac{z-y}{y-x}$
$\frac{z+y}{y-x}$
$\frac{z+x}{y-x}$
A survey shows that $63\%$ of the Americans like cheese whereas $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples, then
In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
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 $\mathrm{K}\, \%$ of them are suffering from both ailments, then $\mathrm{K}$ can not belong to the set :
In a group of students, $100$ students know Hindi, $50$ know English and $25$ know both. Each of the students knows either Hindi or English. How many students are there in the group?
A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone