Directions (51-54): Read the following information carefully and answer the questions given below.

In society A, some people like three different types of music i.e. jazz, rock & folk. People who like only jazz and only rock are in the ratio of 4:3 respectively and people who like all the three types of music is 15. People who like only folk is 50 and people who like jazz is 140. People who like both jazz & folk is 20 and people who like both rock & folk is 50% more than the people who like both jazz & folk. People who like both jazz & rock is average of people who like both jazz & folk and like both rock & folk.

Find the total number of people who like rock music is what percent of total number of people like only folk music?

Correct Answer: The correct option is 260%.

Let us break down the given information step-by-step to find the total number of people who like rock music and then calculate the required percentage.

Step 1: Extract the given data for the three music preference sets (Jazz, Rock, Folk).

1. Total people who like all three types of music = 15.
2. People who like only Folk = 50.
3. Total people who like Jazz = 140.
4. People who like both Jazz & Folk = 20.
Note: In Venn diagram terminology, "both Jazz & Folk" includes those who like all three music types as well as those who like only Jazz & Folk.
5. People who like both Rock & Folk = 50% more than the people who like both Jazz & Folk.
$\text{Both Rock \& Folk}=20+(50\%\text{of}20)=20+10=30$
6. People who like both Jazz & Rock is the average of people who like both Jazz & Folk and both Rock & Folk.
$\text{Both Jazz \& Rock}=\frac{20+30}{2}=\frac{50}{2}=25$

Step 2: Find the number of people who like only Jazz and only Rock.

The total number of people who like Jazz consists of:
- People who like only Jazz
- People who like both Jazz & Rock only
- People who like both Jazz & Folk only
- People who like all three music types

From the given data:
- People who like all three types = 15.
- People who like both Jazz & Folk only = (Both Jazz & Folk) - (All three) = 20 - 15 = 5.
- People who like both Jazz & Rock only = (Both Jazz & Rock) - (All three) = 25 - 15 = 10.

Now, substitute these into the total count for Jazz (which is 140):
$\text{Total Jazz}=\text{Only Jazz}+\text{Jazz \& Rock only}+\text{Jazz \& Folk only}+\text{All three}$
$140=\text{Only Jazz}+10+5+15$
$140=\text{Only Jazz}+30$
$\text{Only Jazz}=140-30=110$

We are given that the ratio of people who like only Jazz to only Rock is 4:3.
$\frac{\text{Only Jazz}}{\text{Only Rock}}=\frac{4}{3}$
$\frac{110}{\text{Only Rock}}=\frac{4}{3}$
$\text{Only Rock}=\frac{110\times 3}{4}=82.5$

Step 3: Calculate the total number of people who like Rock music.

First, find the number of people who like both Rock & Folk only:
- People who like both Rock & Folk only = (Both Rock & Folk) - (All three) = 30 - 15 = 15.

Total people who like Rock music is the sum of:
- Only Rock = 82.5
- Both Jazz & Rock only = 10
- Both Rock & Folk only = 15
- All three = 15

$\text{Total Rock}=82.5+10+15+15=130$

Step 4: Calculate the required percentage.

We need to find what percent the total number of people who like Rock music is of the total number of people who like only Folk music (50):
$\text{Percentage}=\left(\frac{\text{Total Rock}}{\text{Only Folk}}\right)\times 100$
$\text{Percentage}=\left(\frac{130}{50}\right)\times 100=130\times 2=260\%$

Thus, the total number of people who like rock music is 260% of the people who like only folk music.