What is Venn diagram?
Venn diagram is a simple way to represent or explain the relation between sets with the help of diagram.
3 to 4 types are Venn diagram
When one value is contained in the other value.
Ex: Mumbai in India
When some values are common between two objects.
Generally, this type of question is asked in the exam
Ex: Punjab, Haryana and Chandigarh
When two objects are separate from each other.
Ex: Delhi and Bihar
The following Venn-diagram represents the number of person who can Hindi, English and Punjabi.
A = Number of Persons who can read only Hindi
B = Number of Persons who can read only English
C = Number of Persons who can read only Punjabi
G = Number of Persons who can read all three Languages
D = Number of Persons who can read Hindi and English but not Punjabi
E = Number of Persons who can read Hindi and Punjabi but not English
F = Number of Persons who can read English and Punjabi but not Hindi
D + G = Total number of persons who can read both Hindi and English
E + G = Total number of persons who can read both Hindi and Punjabi
G + F = Total number of persons who can read both Punjabi and English
A + D + E + G = Total number of persons who can read Hindi
B+ D + F+ G = Total number of persons who can read English
C + F + E + G = Total number of persons who can read Punjabi
50 workers in a factory, 20 take teas but not coffee and 24 take tea and coffee. Then, how many takes only coffee?
Total number of workers who take tea= 24
Numbers of workers who take tea but not coffee= 20
Numbers of workers who take both tea and coffee= 24 – 20= 4
Numbers of workers who take coffee but not tea= 50 – 24 = 26
Out of 50 students, 14 are taking English and 35 are taking Chemistry. If five students are in both the classes. How many students are in neither class?
A + 5= 14
A= 14 – 5= 9
B + 5= 35
B= 35 – 5= 30
Total number of students who are taking at least one subjects= A + B + 5 = 9 + 30 + 5= 44
Non-student in class= 50 – 44= 6 students
- A survey shows that 75% of the Indians like apples whereas 65% like bananas. What percentage of Indians like both apples and bananas?
options: A) 40% B) 50% C) 60% D) 70%
- Of the student in a certain class 10 had opted course A, 11 opted course B and 14 opted C, if 3 students had opted all three A, B, C and 20 had opted only one of A, B, C. Then, how many had opted exactly 2 courses?
options: A) 2 B) 3 C) 4 D) 5
- In a group of 100 persons 76 can speak Hindi and 34 can speak English. Find how many can speak both Hindi and English?
options: A) 5 B) 7 C) 9 D) 10
- Ina group of 1000 persons, 760 likes Vanilla flavored ice cream while 320 likes chocolate flavored ice cream. How many of them likes only chocolate flavored ice cream?
options: A) 240 B) 250 C) 260 D) 80
- If 93% Indians like tea and 76% like coffee. How many like both?
options: A) 61 B) 69 C) 71 D) 79
A + C =75 …….I
B + C = 65 ……II
Add I & II
A + B + 2C = 140
But maximum percentage is 100.
That means A + B + C should be 100
Therefore on subtracting 100 from 140 we get 40
That is C = 40%
Means 40% Indian like both apples and bananas.
2. (b) 3
W = 3
Course A = P + U + S + W = 10 ……..i
Course B = Q + U + T + W = 11 ……..ii
Course C = R + T + S + W = 14 .…….iii
P + Q + R = 20
On adding Eqs. i , ii and iii
P + Q + R + 2(S + T + U) + 3W = 10 + 11 + 14
20 + 2(S + T + U) + 3W = 35
2(S + T + U) + 9 = 15
2(S + T + U) = 15 – 9
S + T + U =
S + T + U = 3
S, T and U represents the number of students who had opted for exactly 2 courses.
So , the answer is 3
3. (d) 10
A + B =76
B + C = 34
A + 2B + C = 110 ………. i
Total is A + B + C = 100 …..…..ii
Therefore on subtracting 100 from 110 we get 10
That is B = 10
Means 10 person can speak Hindi and English both.
4. (a) 240
A + B = 320
B + C = 760
A + 2B + C = 1080 ………. i
But total is A + B + C = 1000 …..…..ii
Therefore on subtracting 1000 from 1080 we get 80
That is B = 80
Now, we put the value of B in eq. A+B=320
A + 80 = 320
A = 240
Means 240 person like only chocolate flavored ice-cream
5. (b) 69%
A + B = 93
B + C = 76
A + 2B + C = 169 ………. i
But maximum percentage is A + B + C = 100 …..…..ii
Therefore on subtracting 100 from 169 we get 69
That is B = 69
Means 69% person like both Tea & Coffee.