Question

An investigator interviewed $100$ students to determine the performance of three drinks milk, coffee and tea. The investigator reported that $10$ students take all three drinks milk, coffee and tea; $20$ students take milk and coffee, $30$ students take coffee and tea, $25$ students take milk and tea, $12$ students take milk only, $5$ students take coffee only and $8$ students take tea only. Then the number of students who did not take any of the three drinks is

• A. 10
• B. 20
• C. 25
• D. 30

Answer 1

Answer: (B)

Total drink $=3$ (i.e., milk, coffee, tea).
$10$ students take all $3$ drinks i.e. $n(M\cap C\cap T)=10$

Only $20$ students take milk and coffee
i.e., $n(M\cup C)=20$
and $30$ students take coffee and tea
i.e., $n(C\cup T)=30$
and $25$ students take milk and tea
i.e., $n(M\cup T)=25$
$12$ students take milk only
i.e., $n(M)=12$
$5$ students take coffee only
i.e., $n(C)=5$
and $8$ students take tea only
i.e., $n(T)=8$
Total number of students who take any of the drink is $80$ .
$\therefore$ The number of students who did not take any of three drinks $=100-80=20$