**Venn diagram word problems with 2 circles :**

Here we are going to see how to solve word problems with 2 circles.

**Example 1 :**

In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics?

**Solution :**

Let M = The set of students passed in Mathematics

S = The set of students passed in Science

We may solve the given problem using two methods.

(i) Using formula

(ii) Using venn diagram

**Method 1 : **

Total number of students n (M U S) = 50

Number of students passed in both subjects n(MnS) = 10

Number of students passed in science n (S) = 28

From this, we have to find the number of students who passed in mathematics.

n (M U S) = n (M) + n (S) - n (M n S)

50 = n (M) + 28 - 10

50 = n (M) + 18

Subtract 18 on both sides

50 - 18 = n (M) + 18 - 18

n (M) = 32

Hence the number students passed in Mathematics is 32.

**Method 2 :**

Let "x" be the number of students passed in Mathematics.

By representing the given details in venn diagram, we get

From the Venn diagram

x + 10 + 18 = 50

x = 50 - 28 = 22

Number of students passed in Mathematics

= x + 10 = 22 + 10 = 32

**Example 2 :**

The population of a town is 10000. Out of these 5400 persons read newspaper A and 4700 read newspaper B. 1500 persons read both the newspapers. Find the number of persons who do not read either of the two papers.

**Solution :**

Let A = The set of persons who read newspaper A

B = The set of persons who read newspaper B

Number of persons who read at least one news paper

= 3900 + 1500 + 3200

= 8600

Total population = 10000

To find the number of persons who do not read either of the two papers, we have to subtract number of persons who read at least one from total population.

= 10000 - 8600

= 1400

Hence the number of persons who do not read either of the two papers is 1400.

**Example 3 :**

In a school, all the students play either Foot ball or Volley ball or both. 300 students play Foot ball, 270 students play Volley ball and 120 students play both games. Find

(i) the number of students who play Foot ball only

(ii) the number of students who play Volley ball only

(iii) the total number of students in the school

**Solution :**

Let A = The set of students who play foot ball

B = The set of students who play volley ball

(i) The number of students who play Foot ball only is 180

(ii)The number of students who play Volley ball only is 150

(iii) The total number of students in the school

= 180 + 120 + 150

= 450

**Example 4 :**

In a School 150 students passed X Standard Examination. 95 students applied for Group I and 82 students applied for Group II in the Higher Secondary course. If 20 students applied neither of the two, how many students applied for both groups?

Solution :

A = The set of students who applied for Group I

B = The set of students who applied for Group II

Number of students who applied at least one group

= 150 - 20

= 130

n (A) = 95, n (B) = 82 and n (A U B) = 130

n (A U B) = n (A) + n (B) - n (A n B)

130 = 95 + 82 - n (A n B)

130 = 177 - n (A n B)

n (A n B) = 177 - 130 ==> 47

Hence the number of students applied for both groups is 47.

- Venn diagram A U B
- Venn diagram A n B
- Venn diagram of A'
- Venn diagram of B'
- Venn diagram of (AUB)'
- Venn diagram of (AnB)'
- Venn diagram of A\B
- Venn diagram of B\A

After having gone through the stuff given above, we hope that the students would have understood "Venn diagram word problems with 2 circles".

Apart from the stuff given above, if you want to know more about "Venn diagram word problems with 2 circles", please click here

Apart from the stuff "Venn diagram word problems with 2 circles", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**