# 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

__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

__Type 3:__

When two objects are separate from each other.

Ex: Delhi and Bihar

__Type 4:__

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**

__Question 1:__

__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?

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:__

__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?

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:__

__Practice Questions:__

- 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

**Solutions:**

#### (a) 40%

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.