Data Interpretation – A chain of departmental stores has outlets in Delhi, Mumbai

A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments – ‘Apparel’, ‘Electronics’, and ‘HomeDecor’. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table.

The following additional information is known.
1. The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.
2. The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in 2019.
3. The sales amounts in the HomeDecor departments were the same for Mumbai and Kolkata in 2018.
4. The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.
5. The total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.
6. The sales amounts in the HomeDecor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.
7. The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.
8. The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.

Q.1 In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?

1. Bengaluru and Delhi
2. Mumbai and Delhi
3. Delhi and Delhi
4. Mumbai and Mumbai

Answer: 3

Q.2 What was the increase in sales amount, in Crore Rupees, in the Apparel department of Mumbai from 2018 to 2019?  

1. 10
2. 8
3. 5
4. 12

Answer: 4

Q.3 Among all the 12 departments (i.e., the 3 departments in each of the 4 cities), what was the maximum percentage increase in sales amount from 2018 to 2019?  

1. 50
2. 25
3. 75
4. 28

  Answer: 50

Q.4 What was the total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores?  

1. 750
2. 600
3. 150
4. 900

  Answer: 4

Solutions:

Given:

From point 1) , 2) and 3 following table can be made where x , y and z are sales amount of respective department in corresponding years. From point 6.
Sales amount of HomeDecor in Delhi in 2018 = 100 – 20 = 80
Sales amount of HomeDecor in Bangaluru in 2018 = 80 – 20 = 60

	Sales Amounts (Crore Rupees)
	Delhi		Mumbai		Bengaluru		Kolkata
	2018	2019	2018	2019	2018	2019	2018	2019
Apparels	x	y	Y		y		X	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	Z	72	60	80	z	54

From point 8.
If sales amount of Apparels in Bangaluru in 2019 was k then
k + y = 2*54 = 108
k = 108 – y

	Sales Amounts (Crore Rupees)
	Delhi		Mumbai		Bengaluru		Kolkata
	2018	2019	2018	2019	2018	2019	2018	2019
Apparels	x	y	Y	m	y	108 – y	X	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	Z	72	60	80	z	54

From point 7.
Y – x = (108 –y )-y
Or 3y – x = 108 ———-1)  and

m –y = 54 –x
m = 54 + y -x

	Sales Amounts (Crore Rupees)
	Delhi		Mumbai		Bengaluru		Kolkata
	2018	2019	2018	2019	2018	2019	2018	2019
Apparels	x	Y	Y	54 + y -x	y	108 – y	X	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	Z	72	60	80	z	54

Now from point 4:-
(98 -78 + 102 -82 +70 – 90 + 100 – 80) = (54 + 108 – y + 54+y –x+ y) – 2x -2y

40 = 216 -3x – y
3x + y = 176 ————2)
From eq 1 and eq 2)
3y – x= 108
3x + y = 176
On solving
y = 50 and x = 42
  From point 5.
(100+72+80+54) – (80+60+2z) = 70
166 – 2z = 70
Or z = 48
Thus the final table will look like ,

	Sales Amounts (Crore Rupees)
	Delhi		Mumbai		Bengaluru		Kolkata
	2018	2019	2018	2019	2018	2019	2018	2019
Apparels	42	50	50	62	50	58	42	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	48	72	60	80	48	54

1^st– 3)
2^nd – required increase = 62 – 50 = 12
3^rd – maximum percentage increase is for HomeDecor , which is = (72 -48)/48 *100 = 50%
4^th) Required sum = (50+98+100)+(62+102+72)+(58+70+80)+(54+100+54) = 900
 

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