In a society, people like three types of music: jazz, rock, and folk. The number of people who like only jazz and only rock are in the ratio 4 : 3 4:3...

In a society, people like three types of music: jazz, rock, and folk. The number of people who like only jazz and only rock are in the ratio $4:3$ respectively. The number of people who like all three types of music is $15$. The number of people who like only folk is $50$, and the total number of people who like jazz is $140$. The number of people who like both jazz and folk is $20$. The number of people who like both rock and folk is $50$ more than those who like both jazz and folk. The number of people who like both jazz and rock is the average of the number of people who like both jazz and folk and both rock and folk. What is the number of people who like only rock?
Find the respective ratio of total number of people who like both jazz & folk music to that of both rock & jazz music.