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 only jazz music is how much more/less than the total number of people who like at least two types of music.

The correct option is 10.

Let us break down the given information step-by-step using set theory and Venn diagram concepts for the three music types: Jazz, Rock, and Folk.

Step 1: Extract the given data for each region

1. People who like all three types of music = 15

2. People who like only Folk = 50

3. People who like both Jazz & Folk (only) = 20

4. People who like both Rock & Folk (only) is 50% more than people who like both Jazz & Folk (only):

$\text{People who like both Rock \& Folk (only)}=20+(50\%\text{of}20)=20+10=30$

5. People who like both Jazz & Rock (only) is the average of people who like both Jazz & Folk (only) and both Rock & Folk (only):

$\text{People who like both Jazz \& Rock (only)}=\frac{20+30}{2}=25$

Step 2: Calculate the number of people who like only Jazz music

The total number of people who like Jazz is given as 140.

Total Jazz = (Only Jazz) + (Only Jazz & Rock) + (Only Jazz & Folk) + (All three)

$140=\text{Only Jazz}+25+20+15$

$140=\text{Only Jazz}+60$

$\text{Only Jazz}=140-60=80$

Step 3: Calculate the total number of people who like at least two types of music

People who like at least two types of music include those who like exactly two types of music plus those who like all three types of music:

At least two types = (Only Jazz & Rock) + (Only Jazz & Folk) + (Only Rock & Folk) + (All three)

$\text{At least two types}=25+20+30+15=90$

Step 4: Find the required difference

We need to find how much the total number of people who like only jazz music is more/less than the total number of people who like at least two types of music:

$\text{Difference}=90-80=10$

Thus, the number of people who like only jazz music is 10 less than the number of people who like at least two types of music.