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.
Sales Amounts (Crore Rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparels
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
100
72
80
54
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.
Question: 1
In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?
From 1, Consider 'a' as the sales amounts in the Apparel departments for Delhi and Kolkata in 2018. From 2, Consider 'b' as the sales amounts in the Apparel departments for Mumbai, Bengaluru, and Delhi in 2018. From 3, Consider 'c' as the sales amounts in the Home Decor departments for Mumbai and Kolkata in 2018 and that of Delhi and Bengaluru be s and t respectively. Let the sales amounts in the Apparel departments for Mumbai and Bengaluru in 2019 be denoted by 'm' and 'n' respectively. Now, the table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
a
b
b
m
b
n
a
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
s
100
c
72
t
80
c
54
From 6, we get s = 80 and t = 60. From 5, we have : s + c + t + c + 70 = 306 ⇒ 2c = 96 ⇒ c = 48. From 4, (b - a)+(m - b)+(n - b)+(54 - a) =(20) + 20 - 20 + 20 ⇒ 54 + m + n - 2a - b =40. ⇒ 2a + b =14 + m + n ⇒ 2b = 28 + 2m + 2n - 4a … (i) From 7, b - a = n - b ⇒ 2b = a + n ...(ii) and m - b = 54 - a ⇒ a + m = 54 + b ⇒ 2b = 2a + 2m - 108 ...(iii) From 8, 108 = b + n ⇒ 2b = 216 - 2n ...(iv) From (i) and (ii), we get : 28 + 2m + 2n - 4a = 2a + 2m - 108 ⇒ 6a = 136 + 2n ⇒ 3a = 68 + n ...(v) From (ii) and (iv), we get : 216 - 2n = a + n. ⇒ a + 3n = 216 ⇒ 3a = 648 - 9n ...(vi) From (v) and (vi), we get : 648 - 9n = 68 + n ⇒ n = 58 ⇒ a = 42 ⇒ b = 50 ⇒ m = 62 Final table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
42
50
50
62
50
58
42
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
80
100
48
72
60
80
48
54
From the above table ,we can see that in 2018 and 2019, Delhi has the highest sales amount as 80 and 100 respectively.
So, the correct option is (A) : Delhi and Delhi.
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Question: 2
What was the increase in sales amount, in Crore Rupees, in the Apparel department of Mumbai from 2018 to 2019?
From 1, Consider 'a' as the sales amounts in the Apparel departments for Delhi and Kolkata in 2018. From 2, Consider 'b' as the sales amounts in the Apparel departments for Mumbai, Bengaluru, and Delhi in 2018. From 3, Consider 'c' as the sales amounts in the Home Decor departments for Mumbai and Kolkata in 2018 and that of Delhi and Bengaluru be s and t respectively. Let the sales amounts in the Apparel departments for Mumbai and Bengaluru in 2019 be denoted by 'm' and 'n' respectively. Now, the table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
a
b
b
m
b
n
a
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
s
100
c
72
t
80
c
54
From 6, we get s = 80 and t = 60. From 5, we have : s + c + t + c + 70 = 306 ⇒ 2c = 96 ⇒ c = 48. From 4, (b - a)+(m - b)+(n - b)+(54 - a) =(20) + 20 - 20 + 20 ⇒ 54 + m + n - 2a - b =40. ⇒ 2a + b =14 + m + n ⇒ 2b = 28 + 2m + 2n - 4a … (i) From 7, b - a = n - b ⇒ 2b = a + n …....(ii) and m - b = 54 - a ⇒ a + m = 54 + b ⇒ 2b = 2a + 2m - 108 …...(iii) From 8, 108 = b + n ⇒ 2b = 216 - 2n …....(iv) From (i) and (ii), we get : 28 + 2m + 2n - 4a = 2a + 2m - 108 ⇒ 6a = 136 + 2n ⇒ 3a = 68 + n …....(v) From (ii) and (iv), we get : 216 - 2n = a + n. ⇒ a + 3n = 216 ⇒ 3a = 648 - 9n ….....(vi) From (v) and (vi), we get : 648 - 9n = 68 + n ⇒ n = 58 ⇒ a = 42 ⇒ b = 50 ⇒ m = 62 Final table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
42
50
50
62
50
58
42
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
80
100
48
72
60
80
48
54
From the table, we can see that, Apparel Department of Mumbai is having 62 and 50 sales, in Crore rupees in 2018 and 2019 respectively. Increase in sales from 2018 to 2019 : = 62 - 50 = 12
So, the correct option is (A) : 12.
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Question: 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?
From 1, Consider 'a' as the sales amounts in the Apparel departments for Delhi and Kolkata in 2018. From 2, Consider 'b' as the sales amounts in the Apparel departments for Mumbai, Bengaluru, and Delhi in 2018. From 3, Consider 'c' as the sales amounts in the Home Decor departments for Mumbai and Kolkata in 2018 and that of Delhi and Bengaluru be s and t respectively. Let the sales amounts in the Apparel departments for Mumbai and Bengaluru in 2019 be denoted by 'm' and 'n' respectively. Now, the table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
a
b
b
m
b
n
a
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
s
100
c
72
t
80
c
54
From 6, we get s = 80 and t = 60. From 5, we have : s + c + t + c + 70 = 306 ⇒ 2c = 96 ⇒ c = 48. From 4, (b - a)+(m - b)+(n - b)+(54 - a) =(20) + 20 - 20 + 20 ⇒ 54 + m + n - 2a - b =40. ⇒ 2a + b =14 + m + n ⇒ 2b = 28 + 2m + 2n - 4a ….… (i) From 7, b - a = n - b ⇒ 2b = a + n …....(ii) and m - b = 54 - a ⇒ a + m = 54 + b ⇒ 2b = 2a + 2m - 108 …....(iii) From 8, 108 = b + n ⇒ 2b = 216 - 2n …....(iv) From (i) and (ii), we get : 28 + 2m + 2n - 4a = 2a + 2m - 108 ⇒ 6a = 136 + 2n ⇒ 3a = 68 + n ….....(v) From (ii) and (iv), we get : 216 - 2n = a + n. ⇒ a + 3n = 216 ⇒ 3a = 648 - 9n ……...(vi) From (v) and (vi), we get : 648 - 9n = 68 + n ⇒ n = 58 ⇒ a = 42 ⇒ b = 50 ⇒ m = 62 Final table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
42
50
50
62
50
58
42
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
80
100
48
72
60
80
48
54
From the above table , we can see that Home decor department of Mumbai has got the highest percentage increase in sales from 2018 to 2019. Percentage Increase = \(\frac{72-48}{48}\times100\) \(=\frac{24}{48}\times100\) \(=50\)
So, the correct option is (B) : 50.
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Question: 4
What was the total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores?
From 1, Consider 'a' as the sales amounts in the Apparel departments for Delhi and Kolkata in 2018. From 2, Consider 'b' as the sales amounts in the Apparel departments for Mumbai, Bengaluru, and Delhi in 2018. From 3, Consider 'c' as the sales amounts in the Home Decor departments for Mumbai and Kolkata in 2018 and that of Delhi and Bengaluru be s and t respectively. Let the sales amounts in the Apparel departments for Mumbai and Bengaluru in 2019 be denoted by 'm' and 'n' respectively. Now, the table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
a
b
b
m
b
n
a
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
s
100
c
72
t
80
c
54
From 6, we get s = 80 and t = 60. From 5, we have : s + c + t + c + 70 = 306 ⇒ 2c = 96 ⇒ c = 48. From 4, (b - a)+(m - b)+(n - b)+(54 - a) =(20) + 20 - 20 + 20 ⇒ 54 + m + n - 2a - b =40. ⇒ 2a + b =14 + m + n ⇒ 2b = 28 + 2m + 2n - 4a ….… (i) From 7, b - a = n - b ⇒ 2b = a + n ….....(ii) and m - b = 54 - a ⇒ a + m = 54 + b ⇒ 2b = 2a + 2m - 108 ……...(iii) From 8, 108 = b + n ⇒ 2b = 216 - 2n ….....(iv) From (i) and (ii), we get : 28 + 2m + 2n - 4a = 2a + 2m - 108 ⇒ 6a = 136 + 2n ⇒ 3a = 68 + n ……...(v) From (ii) and (iv), we get : 216 - 2n = a + n. ⇒ a + 3n = 216 ⇒ 3a = 648 - 9n ….....(vi) From (v) and (vi), we get : 648 - 9n = 68 + n ⇒ n = 58 ⇒ a = 42 ⇒ b = 50 ⇒ m = 62 Final table will be as follows :
Sales Amounts (Crore rupees)
Delhi
Mumbai
Bengaluru
Kolkata
2018
2019
2018
2019
2018
2019
2018
2019
Apparel
42
50
50
62
50
58
42
54
Electronics
78
98
82
102
90
70
80
100
Home Decor
80
100
48
72
60
80
48
54
From the above table ,we can see that the Departmental Stores has following sales amount in 2019 : Delhi = 50 + 98 + 100 = 248 Mumabi = 62 + 102 + 72 = 236 Bengaluru = 58 + 70 + 80 = 208 Kolkata = 54 + 100 + 54 = 208 Therefore, total sales amount in 2019 = 248 + 236 + 208 + 208 = 900.
