Explanation:
According to the given information, there are 80 IDusic lovers, out of which 40 people liked modern songs and 30% liked modern but not folk songs.
(a) To find the number of people who liked modern songs only, we need to subtract the number of people who liked both modern and folk songs from the total number of people who liked modern songs. Let's assume the number of people who liked both types of songs is 'x'.
So, the number of people who liked modern songs only = (Total number of people who liked modern songs) - x
= 40 - x
Now, we know that 30% of the total number of IDusic lovers liked modern but not folk songs. So, we can write an equation as:
30% of 80 = 40 - x + x + 30% of 80 - 30
Solving this equation, we get:
x = 12
Therefore, the number of people who liked modern songs only = (Total number of people who liked modern songs) - x
= 40 - 12
= 28
(b) To find the number of people who liked both types of songs, we already have 'x' from the previous calculation. So, the number of people who liked both types of songs = 12.
(c) If 30 people liked folk songs only, then we can find the number of people who did not like both types of songs as follows:
Number of people who did not like both types of songs = Total IDusic lovers - (Number of people who liked modern but not folk songs + Number of people who liked folk songs only + Number of people who liked both types of songs)
= 80 - (30% of 80 + 30 + 12)
= 18
(d) If each person liked at least one type of song, then the total number of IDusic lovers who liked folk songs can be calculated as follows:
Number of people who liked folk songs = Total IDusic lovers - Number of people who did not like both types of songs
= 80 - 18
= 62