Question

An investigator interviewed $100$ students to determine their preferences for the three drinks: milk $\left(M\right)$, coffee $\left(C\right)$ and tea $\left(T\right)$. He reported the following: $10$ students had all the three drinks $M,C,T;20$ had $M$ and $C$ only; $30$ had $C$ and $T;25$ had $M$ and $T;12$ had $M$ only; $5$ had $C$ only, $8$ had $T$ only. Using a venn diagram, find how many did not take any of the three drinks?

Answer 1

$10$ students had all the $3$ drinks (M & C & T)

$20$ had M & C $=20-$(M & C & T)

$=20-10=10$

$30$ had C & T $=30-$(M & C & T)

$=30-10=20$

$25$ had M & T $=25-$(M & C & T)

$=25-10=15$

$12$ had only M$=12$

$8$ had only T$=8$

$5$ had only C$=5$

Now, we have to odd up all of the little segments along with the 'x'(x is number of students who did not take any drink)

$\therefore 10+10+20+15+12+8+5+x=100$

$80+x=100$

$x=20$

$\therefore 20$ students did not take any drinks.