CAT 2018 Slot 1 — DILR Question 13
Answer the following question based on the information given below.
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.
What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?
Answer & solution
- A
22.22
28.57
- C
38.46
- D
50.00
The sales figures during April, May and June of 2016 form an arithmetic progression. Assuming ‘d’ as common difference, 40 + (40 + d) + (40 + 2d) = 150 ⇒ d = 10
Therefore, sales in May was 50 and that in June was 60.
The sales figures during October, November and December of 2016 form an arithmetic progression. Assuming ‘f’ as common difference, 100 + (100 + f) + (100 + 2f) = 360 ⇒ f = 20
Therefore, sales in November was 120 and that in December was 140.
Let sales in August 2017 and December 2017 be ‘a’ and ‘b’.
∴ 60 + a + 70 = 220 and 150 + 170 + b = 500
∴ a = 90 and b = 180
The values for quarter-wise aggregate sales can be found by simply adding sales values of the corresponding months and for values of for annual sales we need to add either values for all quarter-wise sales of that year or values for all the months of that year.
Thus, we have
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Sales in December 2017 = 180 and Sales in December 2016 = 140
∴ the required percentage = × 100 = 28.57
Hence, option (b).