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 both the companies sold by showroom B is what per cent more than the number of scooters of company X sold by showroom A?
The question asks us to compare the sales of scooters from different showrooms and companies based on the provided distribution data. We have two distributions:
- S1: Distribution of the total number of scooters (Company X + Company Y) sold by 5 showrooms (A, B, C, D, E). The total number of scooters in S1 is 6400.
- S2: Distribution of the number of scooters of only Company X sold by the same 5 showrooms. The total number of scooters in S2 is 3000.
We need to find out how much more (in percentage) the number of scooters of both companies sold by showroom B is compared to the number of scooters of company X sold by showroom A.
Calculating Scooter Sales per Showroom
First, let's calculate the exact number of scooters sold by showroom B (both companies) using S1 and the number of scooters sold by showroom A (only company X) using S2.
| Showroom | S1 (Total Scooters) Percentage | S2 (Company X Scooters) Percentage |
|---|---|---|
| A | 19% | 24% |
| B | 21% | 18% |
| C | 15% | 20% |
| D | 33% | 30% |
| E | 12% | 8% |
| Total | 100% (6400) | 100% (3000) |
Number of Scooters (X + Y) Sold by Showroom B
From distribution S1, showroom B accounts for 21% of the total 6400 scooters.
Number of scooters (X + Y) by showroom B = \(21\% \text{ of } 6400\)
Number of scooters (X + Y) by showroom B = \(\frac{21}{100} \times 6400\)
Number of scooters (X + Y) by showroom B = \(21 \times 64\)
Number of scooters (X + Y) by showroom B = \(1344\)
Number of Scooters (only X) Sold by Showroom A
From distribution S2, showroom A accounts for 24% of the total 3000 scooters of company X.
Number of scooters (X) by showroom A = \(24\% \text{ of } 3000\)
Number of scooters (X) by showroom A = \(\frac{24}{100} \times 3000\)
Number of scooters (X) by showroom A = \(24 \times 30\)
Number of scooters (X) by showroom A = \(720\)
Calculating the Percentage More
Now we need to find out what percentage the number of scooters sold by showroom B (1344) is more than the number of scooters sold by showroom A (720).
First, calculate the difference in the number of scooters:
Difference = (Scooters by showroom B) - (Scooters by showroom A)
Difference = \(1344 - 720 = 624\)
Next, calculate the percentage increase. The percentage is calculated with respect to the number of scooters sold by showroom A (720).
Percentage More = \(\frac{\text{Difference}}{\text{Number of Scooters by Showroom A}} \times 100\%\)
Percentage More = \(\frac{624}{720} \times 100\%\)
Let's simplify the fraction:
\(\frac{624}{720} = \frac{624 \div 8}{720 \div 8} = \frac{78}{90}\)
\(\frac{78}{90} = \frac{78 \div 6}{90 \div 6} = \frac{13}{15}\)
Now substitute the simplified fraction back into the percentage calculation:
Percentage More = \(\frac{13}{15} \times 100\%\)
Percentage More = \(\frac{1300}{15}\%\)
Percentage More = \(\frac{1300 \div 5}{15 \div 5}\% = \frac{260}{3}\%\)
To express this as a mixed number, divide 260 by 3:
\(260 \div 3\)
\(260 = 3 \times 86 + 2\)
So, \(\frac{260}{3} = 86 \frac{2}{3}\)
The number of scooters of both companies sold by showroom B is \(86\frac{2}{3}\%\) more than the number of scooters of company X sold by showroom A.
Revision Table: Scooter Sales Analysis
| Metric | Value | Calculation Source |
|---|---|---|
| Total Scooters (S1) | 6400 | Given data |
| Total Company X Scooters (S2) | 3000 | Given data |
| % S1 for Showroom B | 21% | Given data |
| % S2 for Showroom A | 24% | Given data |
| Scooters (X+Y) Showroom B | 1344 | 21% of 6400 |
| Scooters (X) Showroom A | 720 | 24% of 3000 |
| Difference | 624 | 1344 - 720 |
| Percentage More | \(86\frac{2}{3}\%\) | \(\frac{624}{720} \times 100\%\) |
Additional Information on Percentage Change
Understanding percentage change is crucial for data interpretation problems like this. Percentage change tells us the relative change between an old value and a new value.
- Percentage Increase: Used when the new value is greater than the old value. Formula: \(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%\). This is equivalent to \(\frac{\text{Difference}}{\text{Original Value}} \times 100\%\) when calculating how much 'more' something is compared to the original.
- Percentage Decrease: Used when the new value is less than the old value. Formula: \(\frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \times 100\%\).
- It is very important to correctly identify the 'Old Value' or 'Original Value' which serves as the base for the percentage calculation. In this question, we are asked "what per cent more than the number of scooters of company X sold by showroom A", so the number of scooters sold by showroom A (720) is the base (the 'Original Value').
These types of questions combine data analysis from tables/distributions with basic percentage calculations.
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