Question

A school organised a fresher's party for 60 students of 11th class. It was decided that Coffee, Tea
and Juice will be distributed in the party. It was found that 25 students drink Coffee, 26 drink Tea, 26
drink Juice, 9 drink both Coffee and Juice, 8 drink both Tea and Juice, 11 drink both Coffee and Tea
and 3 students had all three drinks.
(a) Find number of students who drink only coffee
(i) 10
(ii) 6
(iii) 8
(iv) 7
(b) Find number of students who drink coffee and juice but not tea
(i) 5
(i) 6
(iii) 7
(iv) 8
(c) Number of students who had exactly one drink is:
(0) 10
(ii) 20
(iii) 30
(iv) 40
(d) Number of students who had atleast one of the drink
(i) 28
(ii) 60
(iii) 52
(iv) 40
(e) Number of students who did not take any drink :
(0) 8
(ii) 5
(iii) 10
(iv) None of these

Answer 1

Given : A school organised a fresher's party for 60 students of 11th class. It was decided that Coffee, Tea and Juice will be distributed in the party. It was found that

25 students drink Coffee,

26 drink Tea,

26 drink Juice, 9 drink both Coffee and Juice,

8 drink both Tea and Juice,

11 drink both Coffee and Tea

and 3 students had all three drinks.

To Find : number of students who drink only coffee

number of students who drink coffee and juice but not tea

Number of students who had exactly one drink is:

Number of students who had atleast one of the drink

Number of students who did not take any drink :

Solution:

C  = 25

T = 26

J  = 26

C ∩ J  = 9

T ∩ J = 8

C ∩  T = 11

C ∩ J ∩  T = 3

Total = C + T + J - C ∩ J - T ∩ J - C ∩  T + C ∩ J ∩  T  + None

=> 60 = 25 + 26 + 26 - 9 - 8 - 11 +  3 + None

=> None = 8

Number of students who did not take any drink : = 8

number of students who drink only coffee = C - C ∩ J - C ∩  T + C ∩ J ∩  T

= 25 - 9 - 11 + 3

= 8

number of students who drink coffee and juice but not tea

C ∩ J  - C ∩ J ∩  T = 9  -  3  = 6

exactly one drink is:

C + T + J - 2 ( C ∩ J + T ∩ J + C ∩  T) + 3 C ∩ J ∩  T

= 25 + 26 + 26 - 2( 9 + 8 + 11) + 3(3)

= 77 - 56 + 9

= 30

Number of students who had exactly one drink is:  30

Number of students who had atleast one of the drink = Total - Number of students who did not take any drink :

= 60 - 8 = 52

in attached venn diagram read M as J .

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