In a class of 100 students, 60 students like to play cricket, 40 students like to play football, 15 students like both. Then the number of students in the class who neither like playing cricket nor playing football are?

Option 4 : 15

Given:

Total numbers of student in class = 100

Like to play cricket = 60

Like to play football = 40

Like both = 15

Formula used:

n(AUB) = n(A) + n(B) – n(A∩B)

Calculation:

Total number of students in class = 100

Let cricket be A and football be B

Students who like to play cricket, n(A) = 60

Student who like to play football, n(B) = 40

Students who like both n(A∩B) = 15

n(AUB) = n(A) + n(B) – n(A∩B)

⇒ n(AUB) = 60 + 40 – 15

⇒ n(AUB) = 100 – 15

⇒ n(AUB) = 85

Students neither like to play cricket nor football are

⇒ 100 – 85

⇒ 15 

∴ Students neither like play cricket nor football are 15.

Shortcut Trick

Venn diagram

[ alt="F1 Shraddha Ujjwal 28.05.2021 D2" src="//storage.googleapis.com/tb-img/production/21/05/F1_Shraddha_Ujjwal_28.05.2021_D2.png" style="width: 372px; height: 158px;">

⇒ 45 play cricket

⇒ 25 play football

⇒ 15 play both 

Students neither like to play cricket nor football are = 100 – 45 – 25 – 15 = 15

∴ Students neither like play cricket nor football are 15