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% of the students speak neither language, 90% must speak at least one language. Since 72% speak Chinese and 65% can speak English, we know, by Principle of Inclusion-Exclusion, that 72+65-90=47% of the students speak both languages.

-Potato2017