Venn Diagram

VENN DIAGRAM

 

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

 

 

Type 1:

When one value is contained in the other value.

Ex: Mumbai in India

venn diagram

 

 

 

 

 

Type 2:

When some values are common between two objects.

Generally, this type of question is asked in the exam

 Ex: Punjab, Haryana and Chandigarh

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Type 3:

When two objects are separate from each other.

Ex: Delhi and Bihar

 

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Type 4:
The following Venn-diagram represents the number of person who can Hindi, English and Punjabi.

 

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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

 

 

Question 1:

50 workers in a factory, 20 take teas but not coffee and 24 take tea and coffee. Then, how many takes only coffee?

 

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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

 

 

Question 2:

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?

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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

 

 

Practice Questions:

 

  1. 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%

 

  1. 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

 

  1. 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

 

  1. 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

 

  1. If 93% Indians like tea and 76% like coffee. How many like both?

options:  A)  61      B) 69      C) 71     D) 79

 

Solutions:

  1.  (a) 40%

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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

 

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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

 

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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

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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%

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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.

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