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; 25 students take milk and tea; 30 students take coffee 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 three drinks is
(a) 10 (b) 20 (c) 25 (d) 30
[JEE (Orissa) 2003]

Answer 1

Given that,

Total students =100

The performance of three drinks; milk, coffee and tea.

10 students take all three drinks  milk, coffee and tea

20 students take milk and coffee;

25 students take milk and tea;

30 students take coffee and tea;

12 students take milk only

5 students take coffee only

8 students take tea only

We need to calculate the value of $N_{MC}$

Using formula for  $N_{MC}$

$N_{MC}=20-10=10$

We need to calculate the value of $N_{MT}$

Using formula for  $N_{MT}$

$N_{MT}=25-10=15$

We need to calculate the value of $N_{TC}$

Using formula for  $N_{TC}$

$N_{TC}=30-10=20$

We need to calculate the number of students  who take any of the drink

Using given data

$N=N_{M}+N_{C}+N_{T}+N_{MC}+N_{MT}+N_{TC}+N_{MCT}$

Put the value into the formula

$N=12+5+8+10+15+20+10$

$N=80$

We need to calculate the number of students who  did not take any of three drinks

Using given data

$N'=N_{total}-N$

$N'=100-80$

$N'=20$

Hence, The number of students who  did not take any of three drinks are 20

(b) is correct option