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
The number of scooters of company Y sold by showroom E is what percent of the number of scooters of both companies sold by showroom C?
55
Understanding Scooter Sales Distribution Across Showrooms
This problem provides data on the sales of scooters from two companies, X and Y, across five different showrooms (A, B, C, D, and E). We have two sets of percentage distributions:
- S1: Distribution of the total number of scooters sold (Company X + Company Y) by the 5 showrooms. The total number of scooters sold across all showrooms in S1 is 6400.
- S2: Distribution of the number of scooters of only Company X sold by the 5 showrooms. The total number of scooters of Company X sold across all showrooms in S2 is 3000.
The data is presented in the following table:
| Showroom | Total number of scooters sold S1 (in %) | Number of scooters of only company X sold S2 (in %) |
|---|---|---|
| A | 19 | 24 |
| B | 21 | 18 |
| C | 15 | 20 |
| D | 33 | 30 |
| E | 12 | 8 |
Total scooters sold in S1 = 6400
Total scooters of Company X sold in S2 = 3000
Analyzing the Specific Question
The question asks us to find the number of scooters of company Y sold by showroom E as a percentage of the total number of scooters (of both companies) sold by showroom C.
To solve this, we need to calculate two values:
- The number of scooters of company Y sold by showroom E.
- The total number of scooters sold by showroom C.
Then, we will calculate the required percentage using the formula: \(\frac{\text{Value 1}}{\text{Value 2}} \times 100\%\).
Step-by-Step Calculation
Step 1: Calculate Total Scooters Sold by Showroom C
From the S1 distribution, showroom C accounts for \(15\%\) of the total scooters sold (which is 6400).
Total scooters sold by showroom C = \(15\%\) of \(6400\)
Total scooters sold by showroom C = \(\frac{15}{100} \times 6400\)
Total scooters sold by showroom C = \(0.15 \times 6400 = 960\)
So, showroom C sold a total of 960 scooters (Company X + Company Y).
Step 2: Calculate Scooters of Company X Sold by Showroom E
From the S2 distribution, showroom E accounts for \(8\%\) of the total scooters of Company X sold (which is 3000).
Scooters of Company X sold by showroom E = \(8\%\) of \(3000\)
Scooters of Company X sold by showroom E = \(\frac{8}{100} \times 3000\)
Scooters of Company X sold by showroom E = \(0.08 \times 3000 = 240\)
So, showroom E sold 240 scooters of Company X.
Step 3: Calculate Total Scooters Sold by Showroom E
From the S1 distribution, showroom E accounts for \(12\%\) of the total scooters sold (which is 6400).
Total scooters sold by showroom E = \(12\%\) of \(6400\)
Total scooters sold by showroom E = \(\frac{12}{100} \times 6400\)
Total scooters sold by showroom E = \(0.12 \times 6400 = 768\)
So, showroom E sold a total of 768 scooters (Company X + Company Y).
Step 4: Calculate Scooters of Company Y Sold by Showroom E
The total scooters sold by showroom E is the sum of scooters from Company X and Company Y.
Total scooters by E = Scooters of X by E + Scooters of Y by E
Scooters of Y by E = Total scooters by E - Scooters of X by E
Scooters of Y by E = \(768 - 240 = 528\)
So, showroom E sold 528 scooters of Company Y.
Step 5: Calculate the Required Percentage
We need to find what percentage the number of scooters of company Y sold by showroom E (528) is of the total number of scooters sold by showroom C (960).
Required Percentage = \(\frac{\text{Number of Y scooters by E}}{\text{Total scooters by C}} \times 100\%\)
Required Percentage = \(\frac{528}{960} \times 100\%\)
Required Percentage = \(\frac{52800}{960}\%\)
Required Percentage = \(\frac{5280}{96}\%\)
Now, let's perform the division:
\(\frac{5280}{96} = 55\)
So, the number of scooters of company Y sold by showroom E is \(55\%\) of the number of scooters of both companies sold by showroom C.
Conclusion
Based on the calculations using the provided distributions S1 and S2, the number of scooters of company Y sold by showroom E is \(55\%\) of the total number of scooters sold by showroom C.
Revision Table: Scooter Sales Analysis
| Calculation Item | Based On | Calculation | Result |
|---|---|---|---|
| Total scooters sold by Showroom C | S1 % for C (15%) and Total S1 (6400) | \(0.15 \times 6400\) | 960 |
| Scooters of Company X sold by Showroom E | S2 % for E (8%) and Total S2 (3000) | \(0.08 \times 3000\) | 240 |
| Total scooters sold by Showroom E | S1 % for E (12%) and Total S1 (6400) | \(0.12 \times 6400\) | 768 |
| Scooters of Company Y sold by Showroom E | Total by E - X by E | \(768 - 240\) | 528 |
| Y by E as % of Total by C | Calculated values (528 and 960) | \(\frac{528}{960} \times 100\%\) | \(55\%\) |
Additional Information: Data Interpretation Tips
Data interpretation questions require careful reading of the provided information, understanding the tables or charts, and performing accurate calculations. Here are some general tips:
- Always read the directions and the question carefully to understand exactly what is being asked.
- Identify the relevant data points needed from the tables or charts.
- Pay attention to whether percentages are of the total number or a subset. In this case, S1 percentages are of 6400, and S2 percentages are of 3000.
- Break down the problem into smaller, manageable steps, as shown in the solution above.
- Double-check your calculations to avoid errors.
- Make sure your final answer addresses the specific question asked (e.g., a percentage, a specific number, a ratio).
- Practice different types of data interpretation problems involving percentages, ratios, averages, etc., to improve your skills.
This problem involved calculating specific values based on percentages of different totals and then finding one value as a percentage of another, a common technique in data interpretation exercises.
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