Question

An Investigator interviewed hundred students to determine the performance of 3 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; 25 student take milk and Tea; 20 student take coffee and tea; 12 students take milk only 5 students take coffe only and 8 students take tea only. Then find the number of students who did not take any of three drinks .

Answer 1

“100 students” means The Universe (the grand total)
“10 students had all the three drinks” means M&C&T [note: start at the middle]
Realize that M&C includes M&C&T, so thatt has to be subtracted.

“20 had milk and coffee” means M&C = 20-M&C&T = 20-10 = 10

“30 had coffee and tea” means C&T=30-M&C&T = 30-10 = 20

“25 had milk and tea” means M&T=25-M&C&T = 25-10 = 15

That fills in all of the overlapping sections of the diagram. Now, the “only” sections are given.
“12 had milk only” means MilkOnly = 20

“5 had coffee only” means CoffeeOInly = 5

“8 had tea only” means TeaOnly=8

Now, you have to add up all of the little segments along with the None that is outside of the circles to get the total of 100 in the Universe (the entire group)
!0+10+20+15+12+5+8+None=100

O.K., solve for None:
80+None=100
None=20

The number of students that did not take any of the three drinks is 20.