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 difference between the number of scooters of company X and Y sold by showroom A and the total number of scooters of company X sold by showrooms B and E together?
436
Understanding the Scooter Sales Data
The problem provides data on the distribution of scooter sales from five different showrooms (A, B, C, D, and E) for two categories:
- S1: Total number of scooters (companies X and Y) sold, with a total of 6400.
- S2: Number of scooters of only company X sold, with a total of 3000.
The distribution for each showroom is given as a percentage of the respective total. We need to find the difference between two specific quantities calculated from this data.
| Showroom | S1 (Total Scooters) (in%) |
S2 (Company X Scooters) (in%) |
|---|---|---|
| A | 19 | 24 |
| B | 21 | 18 |
| C | 15 | 20 |
| D | 33 | 30 |
| E | 12 | 8 |
Calculating Sales from Showroom A (Company X and Y)
The number of scooters of company X and Y sold by showroom A is the total number of scooters sold by showroom A. This is given by the S1 distribution.
Total S1 scooters = 6400
Percentage of S1 for Showroom A = 19%
Number of scooters from showroom A (X and Y combined) = 19% of 6400
Let's calculate this value:
\( \text{Showroom A (X and Y)} = \frac{19}{100} \times 6400 \)
\( \text{Showroom A (X and Y)} = 19 \times 64 \)
\( \text{Showroom A (X and Y)} = 1216 \)
So, showroom A sold 1216 scooters of company X and Y combined.
Calculating Sales from Showrooms B and E (Company X)
We need the total number of scooters of company X sold by showrooms B and E together. This is given by the S2 distribution.
Total S2 scooters (Company X) = 3000
Percentage of S2 for Showroom B = 18%
Percentage of S2 for Showroom E = 8%
Number of Company X scooters from Showroom B = 18% of 3000
\( \text{Showroom B (Company X)} = \frac{18}{100} \times 3000 \)
\( \text{Showroom B (Company X)} = 18 \times 30 \)
\( \text{Showroom B (Company X)} = 540 \)
Number of Company X scooters from Showroom E = 8% of 3000
\( \text{Showroom E (Company X)} = \frac{8}{100} \times 3000 \)
\( \text{Showroom E (Company X)} = 8 \times 30 \)
\( \text{Showroom E (Company X)} = 240 \)
Total number of Company X scooters from showrooms B and E together:
\( \text{Showrooms B and E (Company X)} = \text{Showroom B (Company X)} + \text{Showroom E (Company X)} \)
\( \text{Showrooms B and E (Company X)} = 540 + 240 \)
\( \text{Showrooms B and E (Company X)} = 780 \)
So, showrooms B and E together sold 780 scooters of company X.
Finding the Difference
The question asks for the difference between the number of scooters of company X and Y sold by showroom A and the total number of scooters of company X sold by showrooms B and E together.
Difference = (Number of scooters from showroom A (X and Y)) - (Number of scooters from showrooms B and E (Company X))
\( \text{Difference} = 1216 - 780 \)
\( \text{Difference} = 436 \)
The difference is 436.
Revision Table: Key Calculations
| Description | Calculation | Value |
|---|---|---|
| Showroom A (X and Y) Sales | \( 19\% \text{ of } 6400 \) | 1216 |
| Showroom B (Company X) Sales | \( 18\% \text{ of } 3000 \) | 540 |
| Showroom E (Company X) Sales | \( 8\% \text{ of } 3000 \) | 240 |
| Showrooms B & E (Company X) Total Sales | \( 540 + 240 \) | 780 |
| Required Difference | \( 1216 - 780 \) | 436 |
Additional Information: Data Interpretation Skills
Data interpretation questions require careful reading of the information provided, understanding what each part of the data represents, and performing calculations based on the specific questions asked. In this case:
- We used percentage values to calculate actual numbers from given totals.
- We distinguished between total sales (S1) and sales of a specific category (S2).
- We combined values from different showrooms as required by the question.
- The final step was a simple arithmetic operation (subtraction) to find the difference.
Practicing with different types of charts, tables, and data distributions helps improve data interpretation speed and accuracy.
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