The school organised a farewell party of 100 students and school management decided three types of drinks distributes in party are Milk (M), Coffee (C) and Tea (T). He reported the following 10 students had all the three drinks M,C,T, 20 had M and C; 30 had C and T, 25 had M and T. 12 had M only; 5 had C only; 8 had T only.
(i) The number of students who did not take any drinks, is
(a) 20 (b) 30 (c) 10 (d) 25
(ii) The number of students who prefer Milk is (a) 47 (b) 45 (c) 53 (d) 50
(iii) The number of students who prefer Coffee is
(a)47 (b) 53 (15 (8) 45 (d) 50
(iv) The number of student who prefer Tea is (a) 51 (b) 53 (c) 50 (d) 47
(v) The number of students who prefer Milk and Coffee but not tea is
(a) 12 (b) 10 (c) 15 (d) 20
Answers
Answer:
1. 10 2. 57 3. 65 4. 73 5. 20
Step-by-step explanation:
1. 10+20+30+25+12+5+8
=110 and if we subtract 100-110 then 10
2. 10+20+25+12
=57 cant figure out any of them
3. 10+20+30+5
= 65 cant figure out
4.10+30+25+8
= 73 cant figure out either
5. 20
Given:
At a farewell party of 100 students, the management decides to provide three types of drink tea, coffee, and milk. 10 of the students prefer all the three drinks, 20 prefer both milk and coffee, 30 prefer coffee and tea, 25 prefer tea and coffee, 12 prefer milk only, 5 prefer coffee only and 8 prefer tea only.
To Find:
(i) The number of students who did not take any drinks,
(ii) The number of students who prefer Milk is,
(iii) The number of students who prefer Coffee is,
(iv) The number of students who prefer Tea,
(v) The number of students who prefer Milk and Coffee but not tea,
Solution:
1. It is given that 10 students prefer all the drinks, the number of students who only prefer tea or coffee are,
=> 30 - 10 = 20 ( 10 is subtracted because of repetition for the second time),
2. The total number of students who prefer only milk and tea are,
=> 25 -10 = 15,
3. The total number of students who prefer only coffee and milk are,
=> 20 - 10 = 10,
4. The number of students who prefer only tea, milk, and coffee are 8, 12, 5 respectively.
5. The total number of students who do not prefer any drink = 100 - ( 10 + 20 + 15 + 10 + 8 + 12 + 5,
=> Total number of students who do not prefer any drinks = 100 - 80 = 20 (Question 1 option a).
6. Total number of students who prefer milk is 12 + 15 + 10 + 10 = 47 (Question 2 option a).
7. The total number of students who prefer coffee is 5 + 10 + 20 + 10 = 45. (Question 3 option b).
8. The total number of students who prefer tea is 10 + 8 + 15 + 20 = 53. (Question 4 option b).
9. The total number of students who prefer milk and coffee but not tea is 10. (Question 5 option b).
The correct answer for questions i, ii, iii, iv, v are a, a, b, b, b respectively.