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?
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.
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
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
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
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
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?
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
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.
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.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Nature of the roots of a quadratic equation worksheets
MATH FOR KIDS
Time and work word problems
Pythagorean theorem word problems
Converting repeating decimals in to fractions
L.C.M method to solve time and work problems