Study the pie chart and table and answer the questions
Store
Respective ratio of number of linen kurtis to cotton kurtis sold
A
7:5
B
5:6
C
3:2
D
5:3
E
4:3
F
7:3
Distribution of total no. of Kurtis (cotton and linen) sold by six different stores in 2016,where total kurtis sold are 84,000 What is the difference between average number of linen kurtis sold by stores D and E together and average number of cotton kurtis sold by the same stores together?
To find the difference between the average number of linen kurtis and cotton kurtis sold by stores D and E, we follow these steps:
Step-by-Step Calculation:
Determine the total number of kurtis sold by each store using the percentage from the pie chart:
Store D: \(12\%\) of 84,000 = \(0.12 \times 84000 = 10080\)
Store E: \(28\%\) of 84,000 = \(0.28 \times 84000 = 23520\)
Using the ratio provided, determine the number of linen and cotton kurtis sold:
Store D: Ratio of linen to cotton = 5:3
Total parts for Store D = \(5 + 3 = 8\)
Linen kurtis sold by D = \(\frac{5}{8} \times 10080 = 6300\)
Cotton kurtis sold by D = \(\frac{3}{8} \times 10080 = 3780\)
Store E: Ratio of linen to cotton = 4:3
Total parts for Store E = \(4 + 3 = 7\)
Linen kurtis sold by E = \(\frac{4}{7} \times 23520 = 13440\)
Cotton kurtis sold by E = \(\frac{3}{7} \times 23520 = 10080\)
Calculate the average number of linen and cotton kurtis sold by stores D and E together:
Average linen kurtis sold = \(\frac{6300 + 13440}{2} = 9870\)
Average cotton kurtis sold = \(\frac{3780 + 10080}{2} = 6930\)
Find the difference between the average number of linen and cotton kurtis sold:
Difference = \(9870 - 6930 = 2940\)
Therefore, the difference between the average number of linen kurtis sold by stores D and E and the average number of cotton kurtis sold by the same stores together is 2940.
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Approach Solution -2
We are given the distribution of total kurtis sold by six stores. The pie chart shows the percentage of total kurtis sold by each store, and the table provides the respective ratio of linen to cotton kurtis sold by each store.
The total kurtis sold are 84,000. From the pie chart, we can determine the number of kurtis sold by each store. The pie chart percentages are as follows:
Store A: 16%
Store B: 22%
Store C: 8%
Store D: 12%
Store E: 28%
Store F: 14%
Step 1
Calculate the number of kurtis sold by stores D and E. The number of kurtis sold by each store is given by their respective percentage of the total:
Total kurtis sold by Store D = \( 84,000 \times \frac{12}{100} = 10,080 \)
Total kurtis sold by Store E = \( 84,000 \times \frac{28}{100} = 23,520 \)
Step 2
Use the ratio from the table to find the number of linen and cotton kurtis sold.
For Store D, the ratio of linen to cotton kurtis is 5 : 3. This means for every 8 kurtis sold, 5 are linen and 3 are cotton:
Total number of linen kurtis sold by Store D = \( \frac{5}{8} \times 10,080 = 6,300 \)
Total number of cotton kurtis sold by Store D = \( \frac{3}{8} \times 10,080 = 3,780 \)
For Store E, the ratio of linen to cotton kurtis is 4 : 3. This means for every 7 kurtis sold, 4 are linen and 3 are cotton:
Total number of linen kurtis sold by Store E = \( \frac{4}{7} \times 23,520 = 13,440 \)
Total number of cotton kurtis sold by Store E = \( \frac{3}{7} \times 23,520 = 10,080 \)
Step 3
Calculate the average number of linen and cotton kurtis sold by D and E together.
Average number of linen kurtis sold by D and E together:
