In a class of 120 students, 70 students like to play Guitar, 50 students like to play Piano, 20 students like both. Then the number of students in the class who neither like playing Guitar nor playing Piano are.
In a class of 120 students, 70 students like to play Guitar, 50 students like to play Piano, 20 students like both. Then the number of students in the class who neither like playing Guitar nor playing Piano are. Correct Answer 20
Given:
Total numbers of student in class = 120
Like to play Guitar = 70
Like to play Piano = 50
Like both = 20
Formula used:
n(AUB) = n(A) + n(B) – n(A∩B)
Calculation:
Total number of students in class = 120
Let Guitar denotes be A and Piano be B
Students who like to play Guitar n(A) = 70
Student who like to play Piano n(B) = 50
Students who like both n(A∩B) = 20
n(AUB) = n(A) + n(B) – n(A∩B)
⇒ n(AUB) = 70 + 50 – 20
⇒ n(AUB) = 120 – 20
⇒ n(AUB) = 100
Students neither like playing Guitar nor playing Piano are
⇒ 120 – 100
⇒ 20
∴ Students neither like playing Guitar nor playing Piano are 20.
