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 $=100-80=20$