Question
Download Solution PDFComprehension
Directions: Read the data carefully and answer the following questions.
The table shows the total songs (Classical and Western) downloaded by two persons (A and B) in Quarter 1 and Quarter 2. The table also shows the ratio of Classical and Western songs downloaded by these persons in the given quarters.
| A | B | ||||
| Quarters | Total Songs downloaded | Ratio of Classical to Western | Quarters | Total Songs downloaded | Ratio of Classical to Western |
| Q1 | 78 | 5:8 | Q1 | 66 | 6:5 |
| Q2 | 96 | 3:5 | Q2 | 108 | 1:2 |
What is the average number of Western songs downloaded per quarter by Person A and Person B combined across Q1 and Q2?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGeneral 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,
| Person | Quarter | Total Songs | Classical | Western |
|---|---|---|---|---|
| A | Q1 | 78 | 30 | 48 |
| A | Q2 | 96 | 36 | 60 |
| B | Q1 | 66 | 36 | 30 |
| B | Q2 | 108 | 36 | 72 |
Calculations:
Person A's Western Songs:
Q1: 48
Q2: 60
Total: 48 + 60 = 108
Person B's Western Songs:
Q1: 30
Q2: 72
Total: 30 + 72 = 102
Combined Western Songs (A + B):
108 (A) + 102 (B) = 210
Average per Quarter:
Total quarters = 4 (2 quarters × 2 persons)
Average = 210 / 4 = 52.5
Thus, the correct answer is 52.5.
Last updated on Jul 3, 2025
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