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.
1. What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?
2. In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?
3. During which quarter was the percentage decrease in sales from the previous quarter’s sales the highest?
4. During which month was the percentage increase in sales from the previous month’s sales the highest?
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
x = 10
April 2016 = 40; May 2016 = 50; June 2016 = 60
Also, the same case holds for October, November, December of 2016.
100 + (100 + y) + (100 + 2y) = 360
y = 20
October 2016 = 100; November 2016 = 120; December 2016 = 140
Sales in December 2017 = 500 - 170 - 150 = 180
Sales in December 2016 = 140
Percentage increase = 40/140 × 100 = 28.57%