Question

In a class, 80% of the students play cricket, 85% play football and 75% play both cricket and football. If 40 students
do not play either cricket or football, find the total number of students.​

Answer 1

Step-by-step explanation:

So 80 of them play either football or cricket, and 0.35 x 80 = 28 students play only cricket. So 80 - 28 = 52 students play football (note: any of these 52 students can play only football or both football and cricket). Therefore, the percent of students who play football is 52/100 = 52%.

Answer 2

Concept:

Set theory is the branch of mathematical logic that studies sets.

Given:

We are given that:

80% of the students play cricket

85% play football

75% play both cricket and football

40 students do not play either cricket or football.

Find:

We need to find the total number of students.​

Solution:

P(C) = 80% = 0.8

P(F) = 85% = 0.85

P( C ∩ F) = 75% = 0.75

P( C ∪ F ) = P(C) +P(F) - P(C ∩ F)

P( C ∪ F ) = 0.8 + 0.85 - 0.75 = 0.9

P'( C ∪ F ) = 1 - P( C ∪ F ) =1 - 0.9 = 0.1

Let the total number of students be x

ATQ:

0.1 x = 40

x = 400.

Therefore, we get that the total number of students are 400. ​

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