The multi-layered pie-chart below shows the sales of LED television sets for a big retail electronics outlet during 2016 and 2017. The outer layer shows the monthly sales during this period, with each label showing the month followed by sales figure of that month. For some months, the sales figures are not given in the chart. The middle-layer shows quarter-wise aggregate sales figures (in some cases, aggregate quarter-wise sales numbers are not given next to the quarter). The innermost layer shows annual sales. It is known that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression, as do the three monthly sales figures in the fourth quarter (October, November, December) of that year.
Question: 1
What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?
It is given that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression. So 40 + (40 + x) + (40 + 2x) = 150 Or x = 10 April 2016 = 40 May 2016 = 50 June 2016 = 60 Also, the same case holds for October, November, December of 2016. 100 + (100 + x) ++ (100 + 2x) = 360 Or x = 20 October 2016 = 100 November 2016 = 120 December 2016 = 140 Sales in December 2017 = 180 Sales in December 2016 = 140 Percentage increase = 40/100 × 100 = 28.57%
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Question: 2
In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?
→ Q1 of 2017 compared with Q4 of 2016 = 380-360/360 ×100 = 5.55% increase. →Q2 of 2016 compared with Q1 of 2016 = 150-240/240 × 100 = -37.5% increase or 37.5% decrease → Q4 of 2017 with compared with Q3 of 2017 There is an increase from 220 to 500 . → Q2 of 2017 with compared with Q1 of 2017 = 200-380/380×100 = -47.36 or 47.36% decrease So, sales of Q2 of 2017 ,had the highest percentage decrease compared with Q1 of 2017 .
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Question: 4
During which month was the percentage increase in sales from the previous month’s sales the highest?
Now, let's delve into the two Arithmetic Progressions. It is established that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression, as do the three monthly sales figures in the fourth quarter (October, November, December) of that year. In an arithmetic progression, the middle term is the average of the three terms. Therefore, the sales figure for May 2016 is 50, and for November 2016, it should be 120.
Now, we can determine the sales figures for June and December as well.
We are comparing the sales figures of 40/60, 45/55, 80/70, and 60/100.
Among these, 8070 is the highest, as it exceeds 1. Therefore, October 2017 has the highest percentage increase in sales when compared to the previous month. Hence, the answer is October of 2017
