Interpreting Car Sales Data for Percentage Comparison

This detailed solution guides you through comparing car sales figures for Dealer D and Dealer F based on the provided table, focusing on a specific percentage calculation.

Step 1: Extracting Crucial Car Sales Figures

We need to identify the sales data for Dealer D and Dealer F for the specified periods from the given table.

Calculating Total Sales for Dealer D (February - April)

To find the total sales for Dealer D during the months of February, March, and April, we sum the values from the table:

Total D Sales = $101 + 96 + 103 = 300$ cars.

Calculating Total Sales for Dealer F (January - May)

Similarly, we sum the sales for Dealer F across all five months (January to May) as listed in the table:

Total F Sales = $106 + 99 + 110 + 113 + 112 = 540$ cars.

Step 2: Calculating the Reference Value

The question asks us to compare Dealer D's sales to 'two-third of the total number of cars sold by dealer F in the given 5 months'. Let's calculate this reference value.

Reference Value = $\frac{2}{3} \times \text{Total F Sales}$

Substituting the total sales for Dealer F:

Reference Value = $\frac{2}{3} \times 540$

Performing the calculation:

Reference Value = $2 \times 180 = 360$ cars.

Step 3: Determining the Percentage Less

Now, we need to determine by what percentage Dealer D's sales (300 cars) are less than the calculated Reference Value (360 cars). The comparison is made against the Reference Value.

First, find the absolute difference between the two values:

Difference = Reference Value - Total D Sales

Difference = $360 - 300 = 60$ cars.

Next, calculate the percentage this difference represents relative to the Reference Value (two-third of Dealer F's sales). The formula for percentage less is:

Percentage Less = $\frac{\text{Difference}}{\text{Reference Value}} \times 100\%$

Substituting the values we found:

Percentage Less = $\frac{60}{360} \times 100\%$

Simplify the fraction:

Percentage Less = $\frac{1}{6} \times 100\%$

Calculating the percentage:

Percentage Less = $16.666...\%$

This result can be expressed as a mixed fraction:

Percentage Less = $16\frac{2}{3}\%$

Conclusion on Car Sales Comparison

The analysis shows that the total number of cars sold by dealer D during February to April (300 cars) is $16\frac{2}{3}\%$ less than two-third of the total number of cars sold by dealer F in the given 5 months (360 cars).