In a youth club with 90 members 60 like modern music and 50 like traditional music. The number if them who like both traditional an modern music is three times those who do not like any music. How manybmembers like only one type of music

Answer 1

Let's represent the number of members who like modern music as A, the number of members who like traditional music as B, the number of members who like both modern and traditional music as C, and the number of members who do not like any music as D.

Given:
A = 60
B = 50
C = 3D
Total number of members = 90
A ∪ B = A + B - C + D

Plugging in the values:
60 + 50 - 3D + D = 90
110 - 2D = 90
-2D = -20
D = 10

Now that we have found the value of D, we can find the number of members who like only one type of music:
A = 60
B = 50
C = 3D = 30
D = 10

Members who like only modern music = A - C = 60 - 30 = 30
Members who like only traditional music = B - C = 50 - 30 = 20

Therefore, the number of members who like only one type of music is 30 + 20 = 50.