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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:

In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest? 

 

Option: 1

\mathrm{Q1}


Option: 2

\mathrm{Q2}


Option: 3

\mathrm{Q3}


Option: 4

\mathrm{Q4}


Answers (1)

best_answer

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

From the table constructed, we can observe the below:

Quarter 1:

Sales in 2017 = 380

Sales in 2016 = 240

Quarter 2:

Sales in 2017 = 200

Sales in 2016 = 150

Quarter 3:

Sales in 2017 = 220

Sales in 2016 = 250

Quarter 4:

Sales in 2017 = 500

Sales in 2016 = 360 

Quarter 3 can be eliminated since the sales have decreased from 2016 to 2017.

Increase in Quarter 1 sales \mathrm{= \frac{(380-240)}{240} = \frac{140}{240} = 58.33%}

Increase in Quarter 2 sales \mathrm{= \frac{50}{150} = \frac{1}{3} = 33.33%}

Increase in Quarter 4 sales\mathrm{\frac{\left ( 500-360 \right )}{360}}=\frac{140}{360}

Therefore, Quarter 1 has recorded the highest increase in sales.

 

 

 

Posted by

Ritika Harsh

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