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 respective ratio of total number of people who like both jazz & folk music to that of both rock & jazz music.

Correct Option: 4:5

Step-by-Step Explanation:

Let us analyze the given information step-by-step to extract the data needed for finding the required ratio:

1. People who like all three types of music:

$\text{All three (Jazz ∩ Rock ∩ Folk)}=15$

2. People who like both Jazz & Folk:

From the problem text, the total number of people who like both Jazz & Folk is given directly as 20.

$\text{Both Jazz \& Folk}=20$

3. People who like both Rock & Folk:

It is stated that the number of people who like both Rock & Folk is 50% more than those who like both Jazz & Folk.

$\text{Both Rock \& Folk}=20+(50\%\text{ of }20)=20+10=30$

4. People who like both Jazz & Rock:

It is stated that the number of people who like both Jazz & Rock is the average of people who like both Jazz & Folk and those who like both Rock & Folk.

$\text{Both Jazz \& Rock}=\frac{20+30}{2}=\frac{50}{2}=25$

5. Calculating the required ratio:

We are asked to find the ratio of the total number of people who like both Jazz & Folk music to that of both Rock & Jazz music.

$\text{Ratio}=\frac{\text{Both Jazz \& Folk}}{\text{Both Rock \& Jazz}}=\frac{20}{25}$

Dividing both the numerator and denominator by their greatest common divisor, 5:

$\text{Ratio}=\frac{4}{5}=4:5$

Thus, the required ratio is 4:5.