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. The number of people who like all three types is 15. The number of people who like only folk is 50. 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 total number of people who like rock music as a percentage of the total number of people who like only folk music?

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**Solution:**

1. Let the number of people who like only jazz be $4x$ and only rock be $3x$ (given ratio 4:3).

2. Given:
   - People who like all three types = 15
   - People who like only folk = 50
   - Total people who like jazz = 140
   - People who like both jazz and folk = 20

3. People who like both rock and folk is 50% more than those who like both jazz and folk:
   Rock & Folk = 20 + 0.5 $\times$ 20 = 30

4. People who like both jazz and rock is the average of people who like both jazz & folk and both rock & folk:
  Jazz & Rock= $\frac{20 + 30}{2}$ = 25

5. Total people who like jazz = people who like only jazz + people who like both jazz & rock + people who like both jazz & folk + people who like all three:
   $$140 = 4x + 25 + 20 + 15$$
   $$4x = 140 - 60 = 80$$
   $$x = 20$$

6. Number of people who like only rock:
   $$3x = 3 \times 20 = 60$$

7. Total people who like rock = only rock + both jazz & rock + both rock & folk + all three:
   $$60 + 25 + 30 + 15 = 130$$

8. Required percentage = $
$\frac{\text{Total rock}}{\text{Only folk}} \times 100 = \frac{130}{50} \times 100 = 260\%$$

**Answer:** 260\%

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