What is the ratio of the total number of Classical songs downloaded by person A in both quarters to the total number of Western songs downloaded by person B in both quarters?

General Solution:

We have two persons A and B who downloaded songs in two quarters Q1 and Q2. For each person and quarter, we're given:

Total songs downloaded

Ratio of Classical to Western songs

Calculating Songs by Type for Each Person:

Person A:

Q1:

Total songs: 78

Ratio Classical:Western = 5:8

Total parts = 5 + 8 = 13

Classical songs = 5/13 × 78 = 30

Western songs = 8/13 × 78 = 48

Q2:

Total songs: 96

Ratio = 3:5

Total parts = 3 + 5 = 8

Classical = 3/8 × 96 = 36

Western = 5/8 × 96 = 60

Person B:

Q1:

Total songs: 66

Ratio = 6:5

Total parts = 6 + 5 = 11

Classical = 6/11 × 66 = 36

Western = 5/11 × 66 = 30

Q2:

Total songs: 108

Ratio = 2:3

Total parts = 1 + 2 = 3

Classical = 1/3 × 108 = 36

Western = 2/3 × 108 = 72

Thus,

Calculations:

Calculate total Classical songs for A:

A's Classical in Q1: 30

A's Classical in Q2: 36

Total Classical for A: 30 + 36 = 66

Calculate total Western songs for B:

B's Western in Q1: 30

B's Western in Q2: 72

Total Western for B: 30 + 72 = 102

Find the ratio:

Ratio of A's Classical to B's Western: 66 : 102 = 11 : 17

Thus, the correct answer is 11:17.