Instructions

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 quarterwise 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 53

During which quarter was the percentage decrease in sales from the previous quarter’s sales the highest?

Solution

We have been given details about the quarterly sales figures. Also, we have been given details about the sales figures every month. Some of the data are missing and some additional conditions have been given in the question. Let us try to complete the pie chart as much as possible with the data available to us.

It is known that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression.

We know that the sales in April is 40.

Let the sales in May be 40+x and the sales in June be 40+2x.

We know that the total sales in Q2 is 150.

=> 40 + 40 + x + 40 + 2x = 150

3x = 30

x = 10

Therefore, sales in May 2016 = 40 + 10 = 50

Sales in June 2016 = 40 + 20 = 60

Similarly, it has been given that the sales in October, November, and December 2016 form an arithmetic progression.

Sales in October = 100

Sales in Q4 = 360

Let the sales in November be 100+y and the sales in December be 100+2y.

100 + 100 + y + 100 + 2y = 360

300 + 3y = 360

=> y = 20

Sales in November 2016 = 120 and Sales in December 2016 = 140

Sales in Q1 of 2016 = Sum of the sales in the months of January, February, and March 2016

= 80 + 60 + 100

= 240

Sales in Q3 of 2016 = Sum of the sales in the months of July, August, and September 2016

= 75 + 120 + 55

= 250

Sales in Q1 of 2017 = 120 + 100 + 160 = 380

Sales in Q2 of 2017 = 65 + 75 + 60 = 200

We know that sales in Q3 of 2017 = 220

Let the sales in August of 2017 be ‘a’.

60 + 70 + a = 220

=> a = 90

Sales in August 2017 = 90

We know that sales in Q4 of 2017 = 500

Let the sales in December of 2017 be ‘d’.

150 + 170 + d = 500

=> d = 180

Sales in December 2017 = 180

Q2 of 2017:

Sales in Q2 of 2017 = 200

Sales in Q1 of 2017 = 380

% decrease = 180/380

Q4 of 2017:

We can eliminate this option since the sales has increased in Q4 of 2017 as compared to the previous quarter.

Q2 of 2016:

Sales in Q2 of 2016 = 150

Sales in Q1 of 2016 = 240

% decrease = 90/240

Q1 of 2017:

Sales in Q1 of 2017 has increased as compared to sales in the previous quarter. We can eliminate this option as well.

180/380 is very close to 50%. 90/240 is closer to 33.33%. Therefore, option A is the right answer.

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