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  • 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

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:

 During which month was the percentage increase in sales from the previous month’s sales the highest? 

 

Option: 1

March of 2017 

 

 


Option: 2

October of 2017 
 


Option: 3

October of 2016 

 


Option: 4

March of 2016 


Answers (1)

Let the sales figures for April, May, and June 2016 be a, b, and c, respectively. 

We know that these sales figures form an arithmetic sequence, so we have the equation 

\mathrm{B = a + d,}

where d is the common difference. 

We also know that the average sales figure for this quarter is 150, so we have the equation: \mathrm{3 a+b+c=150}

Substituting the 1st equation into the 2nd equation, we get:

\mathrm{3 a+(a+d)+(a+2 d)=150}

Simplifying this equation, we get:

\mathrm{3a + 3d=450}

We can solve this equation for a to get \mathrm{a=100. }

Substituting this value into the first equation, we get \mathrm{b=100+d. }

Since the average sales figure for October, November, and December 2016 is also 150, we have the equation:

\mathrm{3100+d+\left ( 100+d\right )+\left ( 100+2d \right )=150}

Simplifying this equation, we get:

\mathrm{3d=60}

Solving this equation for d, we get \mathrm{d=20.}

Therefore, the sales figures for April, May, and June 2016 are 40, 50, and 60, respectively.

The sales figures for October, November, and December 2016 are 100, 120, and 140, respectively.

2016 2017
Quarter Month Sale figure Quarter Month Sale figure
Q1 (240) January 80 Q1(380) January 120
February 60 February 100
March 100 March 160
Q2(150) April 40 Q2(200) April 60
May 50 May 75
June 60
June
65
Q3(250) July 75 Q3(220) July 60
August 120 August 90
September 55 September 70
Q4(360) October 100   Q4(500) October 150
November 120 November 170
December 140 December 180

Considering all the options:

  1. March of 2017:

Sales in March of 2017 = 160

Sales in February of 2017 = 100

% increase = \frac{60}{100}\times100 = 60%

 

  1. October of 2017:

Sales in October of 2017 = 150

Sales in September of 2017 = 70

% increase \frac{80}{70}\times100=\sim 115%

  1. March of 2016:

Sales in March of 2016 = 100

Sales in February of 2016 = 60

% increase \frac{40}{60}\times100=66.7%

  1. October of 2016:

Sales in October of 2016 = 100

Sales in September of 2016 = 55

% increase =\frac{45}{55}\times100=\sim 82%

Therefore, %increase in sales for option B is highest.

 

Posted by

Ramraj Saini

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