Question

out of 100 person in a group 72% speak English and 43% speak French each one out of hundred percent speak at least one language then how many speak only English how many speak only friends how many of them speak English and French both

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{A}\mathrm{be}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{people}\mathrm{who}\mathrm{can}\mathrm{speak}\mathrm{English}. \\ \mathrm{Let}\mathrm{B}\mathrm{be}\mathrm{the}\mathrm{setof}\mathrm{people}\mathrm{who}\mathrm{can}\mathrm{speak}\mathrm{French}. \\ \mathrm{Now},\mathrm{n}\left(\mathrm{A}\right)=72;\mathrm{n}\left(\mathrm{B}\right)=43;\mathrm{n}\left(\mathrm{A}\cup \mathrm{B}\right)=100 \\ \mathrm{Now},\mathrm{n}\left(\mathrm{A}\cup \mathrm{B}\right)=\mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right) \\ \Rightarrow 100=72+43-\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right) \\ \Rightarrow \mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right)=72+43-100=15 \\ \mathrm{So},\mathrm{number}\mathrm{of}\mathrm{people}\mathrm{who}\mathrm{cn}\mathrm{speak}\mathrm{both}\mathrm{English}\mathrm{and}\mathrm{French}=15 \\ \mathrm{Number}\mathrm{of}\mathrm{people}\mathrm{who}\mathrm{can}\mathrm{speak}\mathrm{English}\mathrm{only}=\mathrm{n}\left(\mathrm{A}-\mathrm{B}\right) \\ =\mathrm{n}\left(\mathrm{A}\right)-\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right) \\ =72-15 \\ =57 \\ \mathrm{Number}\mathrm{of}\mathrm{people}\mathrm{who}\mathrm{can}\mathrm{speak}\mathrm{French}\mathrm{only}=\mathrm{n}\left(\mathrm{B}-\mathrm{A}\right) \\ =\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right) \\ =43-15 \\ =28 \end{gathered}$$