Question

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

• A. Delhi and Delhi
• B. Mumbai and Mumbai
• C. Bengaluru and Delhi
• D. Mumbai and Delhi
• A. 12
• B. 5
• C. 10
• D. 8
• A. 75
• B. 50
• C. 28
• D. 25
• A. 750
• B. 150
• C. 600
• D. 900

Answer 1

The Correct Option is A

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

So, the correct option is (D) : 900.