2000 PMWC Problems/Problem I5

Problem

In a language college, students can speak Chinese, students can speak English, and students can speak neither Chinese nor English. Find the percentage of students who can speak both Chinese and English.

Solution

Since $10 \text{%}$ (Error compiling LaTeX. Unknown error_msg) of the students speak neither language, $90 \text{%}$ (Error compiling LaTeX. Unknown error_msg) must speak at least one language. Since $72 \text{%}$ (Error compiling LaTeX. Unknown error_msg) speak Chinese and $65 \text{%}$ (Error compiling LaTeX. Unknown error_msg) can speak English, we know, by Principle of Inclusion-Exclusion, that $72+65-90=\boxed{47%}$ (Error compiling LaTeX. Unknown error_msg) of the students speak both languages.

-Potato2017