Explanation:

Let’s break down what’s happening step by step so it makes sense:

- Call people who like only Folk = F, only Rock = R, only Jazz = J.

The ratio F:R:J is 56:79:41

Let’s use x as the common factor.

So, F = 56x, R = 79x, J = 41x.

- People who like both Rock & Jazz but NOT Folk = 50

People who like both Folk & Rock but NOT Jazz = 35

People who like both Folk & Jazz but NOT Rock = Let’s say A.

People who like all three = B.

- Given: “The number of people who prefer to listen both ‘Folk’ and ‘Jazz’ but not ‘Rock’ is 25% less than the number who prefer to listen all three.”

So, A = B – (25% of B) = 0.75B

- We also know:

J = five less than six times of (Folk & Rock but not Jazz)

So, J = 6×35 – 5 = 210 – 5 = 205

- The number of people with exactly two genres:

Exactly two-genres = (People who like both, but not all three)

So, sum of: 35 (Folk & Rock, not Jazz) + 50 (Rock & Jazz, not Folk) + A (Folk & Jazz, not Rock) = 130

35 + 50 + A = 130 ? A = 45

- From before: A = 0.75B

So, 45 = 0.75B ? B = 60

- Earlier, J = 41x = 205 ? x = 5

So:

Only Folk = 56×5 = 280

Only Rock = 79×5 = 395

Only Jazz = 41×5 = 205

Now, to get “people who prefer to listen Folk” — that’s:

Only Folk + (Folk & Rock, not Jazz) + (Folk & Jazz, not Rock) + (All three)

= 280 + 35 + 45 + 60 = 420

Same way, “people who prefer to listen Jazz”:

Only Jazz + (Folk & Jazz, not Rock) + (Rock & Jazz, not Folk) + (All three)

= 205 + 45 + 50 + 60 = 360

Now, ratio “Folk” to “Jazz”:

420 : 360 = 7 : 6

So, option 3 — 7 : 6 — is the answer.

Option 3 (7:6) is correct.