Direction: Read the following information and answer the four items that follow: Let the distribution of the number of scooters of companies X and Y sold by 5 showrooms (A, B, C, D and E) in a certain year be denoted S1 and the distribution of the number of scooters of only company X sold by the five showrooms in the same year be denoted by S2. Showroom A B C D E Total number of scooters sold S1 (in%) 19 21 15 33 12 6400 S2 (in%) 24 18 20 30 8 3000
What is the average number of scooters of company Y sold by the showrooms A, C and E?
Understanding the Scooter Sales Data
The problem provides data on the distribution of scooter sales from two companies, X and Y, across five showrooms (A, B, C, D, and E). Distribution S1 represents the total number of scooters sold by both companies combined (X + Y), and distribution S2 represents the number of scooters sold by company X only. Both distributions are given as percentages of their respective totals.
To find the number of scooters of company Y sold by a specific showroom, we need to subtract the number of scooters of company X (from S2) from the total number of scooters (from S1) for that showroom.
Data Analysis from the Table
The table provides the percentage distribution for S1 (Total X+Y scooters) and S2 (Only X scooters) across the five showrooms. The total number of scooters for S1 is 6400, and for S2 is 3000.
| Showroom | S1 (in %) | S2 (in %) |
|---|---|---|
| A | 19 | 24 |
| B | 21 | 18 |
| C | 15 | 20 |
| D | 33 | 30 |
| E | 12 | 8 |
| Total number of scooters sold | 6400 | 3000 |
Calculating Scooters Sold by Company Y for Showrooms A, C, and E
We need to find the number of scooters sold by company Y in showrooms A, C, and E. This can be calculated for each showroom as follows:
Number of Y scooters = (Percentage in S1 / 100) * Total S1 scooters - (Percentage in S2 / 100) * Total S2 scooters
Showroom A:
- Total scooters (S1) in A = \( \frac{19}{100} \times 6400 \)
- Total scooters (S1) in A = \( 0.19 \times 6400 = 1216 \)
- Scooters of company X (S2) in A = \( \frac{24}{100} \times 3000 \)
- Scooters of company X (S2) in A = \( 0.24 \times 3000 = 720 \)
- Scooters of company Y in A = \( 1216 - 720 = 496 \)
Showroom C:
- Total scooters (S1) in C = \( \frac{15}{100} \times 6400 \)
- Total scooters (S1) in C = \( 0.15 \times 6400 = 960 \)
- Scooters of company X (S2) in C = \( \frac{20}{100} \times 3000 \)
- Scooters of company X (S2) in C = \( 0.20 \times 3000 = 600 \)
- Scooters of company Y in C = \( 960 - 600 = 360 \)
Showroom E:
- Total scooters (S1) in E = \( \frac{12}{100} \times 6400 \)
- Total scooters (S1) in E = \( 0.12 \times 6400 = 768 \)
- Scooters of company X (S2) in E = \( \frac{8}{100} \times 3000 \)
- Scooters of company X (S2) in E = \( 0.08 \times 3000 = 240 \)
- Scooters of company Y in E = \( 768 - 240 = 528 \)
Calculating the Average Number of Y Scooters
Now we have the number of scooters of company Y sold by showrooms A, C, and E. To find the average, we sum these numbers and divide by 3 (the number of showrooms).
- Total Y scooters from A, C, and E = \( 496 + 360 + 528 = 1384 \)
- Average Y scooters = \( \frac{1384}{3} \)
- Average Y scooters = \( 461.333... \)
The average can be expressed as a mixed fraction:
- \( \frac{1384}{3} = \frac{1383 + 1}{3} = \frac{1383}{3} + \frac{1}{3} = 461 + \frac{1}{3} = 461\frac{1}{3} \)
Conclusion
The average number of scooters of company Y sold by the showrooms A, C, and E is \( 461\frac{1}{3} \).
Revision Table: Key Calculations
| Showroom | S1 Value (Total) | S2 Value (Only X) | Y Scooters (S1 - S2) |
|---|---|---|---|
| A | 1216 | 720 | 496 |
| C | 960 | 600 | 360 |
| E | 768 | 240 | 528 |
| Sum (A, C, E) | - | - | 1384 |
| Average (Sum / 3) | - | - | \( \frac{1384}{3} = 461\frac{1}{3} \) |
Additional Information: Percentage and Average Concepts
Understanding Percentages: A percentage represents a part out of a hundred. To calculate a percentage of a total number, you convert the percentage to a decimal (by dividing by 100) and multiply it by the total. For example, 19% of 6400 is \( \frac{19}{100} \times 6400 \).
Calculating Averages: The average (or mean) of a set of numbers is found by summing all the numbers in the set and then dividing the sum by the count of numbers in the set. In this case, we summed the number of Y scooters from three showrooms (A, C, E) and divided by 3.
This problem combines percentage calculations with the concept of finding an average, which is common in data interpretation questions.
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