Read the following information, graph and table and answer the questions that follow.
Ellen Inc. is a Mumbai based company which sells five products branded as A, B, C, D and E in India. Anita looks after entire sales of North India working from regional office in Delhi. She was preparing for annual review meeting scheduled next day in Mumbai. She was attempting to analyse sales in North India for the seven year period from 2009 to 2015. She first calculated average sales in rupees of all the five brands and constructed a table exhibiting the difference between average sales of each pair of brands as shown in the following table:
Average Sales of Product A minus Average Sales of Product B
After taking a print out of the above table, she attempted to look at the trend of sales and plotted a graph in MS Excel. Later she took a print out of the graph and left for a meeting. While on her way she figured out that due to some printer cartridge problem sales of Product A in 2013, Product C in 2010, and Product D in 2012 were not visible in the graph as reproduced below. Anita had to make some quick calculations to arrive at the information outlined in the following question.
What are the sales of Product A in 2013, Product C in 2010 and Product D in 2012?
Let's tabulate the chart ,
Since difference in average sales is given , Difference in sales can be found by multiplying it by 7
For example
Let the sales of A be $$a_1,a_2,a_3,a_4,a_5,a_6,a_7$$ in 2009 - 2015 respectively.
Let the sales of B be $$b_1,b_2,b_3,b_4,b_5,b_6,b_7$$
Given that $$\frac{\left(a_1+a_2+a_3+a_4+a_5+a_6+a_7\right)}{7}-\frac{\left(b_1+b_2+b_3+b_4+b_5+b_6+b_7\right)}{7}=214.29$$
Hence A- B = 214.29 * 7 = 1500
Similarly, all the remaining differences in sales can be calculated
Let the sales of A in 2013 be 'a', C in 2010 be 'c', D in 2012 be 'd' .
Total sales of A = (6800+a)
B = 5800
C = (7400+c)
D = (5700+d)
E = 7000
A - B = 6800+a - 5800 = 1500 => a = 500 crores
B - C = 5800 - 7400 - c = -2400 => c = 800 crores
D - E = 5700 + d - 7000 = -700 => d = 600 crores
Hence C is the correct answer.
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