Question

In a survey of a group of student ,it was found that 45%of them liked literature ,70% liked music and 15%liked none.
1.Repesent the above information in a venn diagram
2.if 60 student liked both the subjects ,find the number of students participated in the survey.

Answer 1

2. The number of students who participated in the survey is 171.

1. To represent the information given in the survey in a Venn diagram, we need to consider three sets: literature, music, and the complement of both (none). The Venn diagram will illustrate the overlapping regions.

Venn Diagram:

Let's label the sets as follows:

Set A represents the students who like literature.

Set B represents the students who like music.

Set C represents the students who like none.

The overlapping region between sets A and B represents the students who like both literature and music.

The Venn diagram will look like this:

  A: Literature

________

|        |

|   AB   |

|________|

/

B: Music C: None

Calculation of Total Participants:

Given that 60 students liked both literature and music (AB), we can calculate the number of students who participated in the survey as follows:

2. Let X be the total number of participants.

Number of students who liked literature (A) = 45% of X = 0.45X

Number of students who liked music (B) = 70% of X = 0.70X

Number of students who liked none (C) = 15% of X = 0.15X

Since 60 students liked both literature and music, we can write the equation:

0.45X + 0.70X - 60 = X - (0.45X + 0.70X + 0.15X)

Simplifying the equation:

1.15X - 60 = 0.70X + 0.45X + 0.15X

0.95X - 60 = 1.30X

0.35X = 60

X = 60 / 0.35

X ≈ 171.43

Rounding to the nearest whole number, we find that approximately 171 students participated in the survey.

For more such questions on survey visit:

https://brainly.in/question/32398673

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