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

Define 'a' as the 2018 Apparel sales in Delhi and Kolkata. Define 'b' as the 2018 Apparel sales in Mumbai, Bengaluru, and Delhi. Define 'c' as the 2018 Home Decor sales in Mumbai and Kolkata, with Delhi's and Bengaluru's sales being 's' and 't' respectively. Let 'm' and 'n' represent the 2019 Apparel sales in Mumbai and Bengaluru, respectively. The sales data is presented in the following table:

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 source 6, s = 80 and t = 60. From source 5, the equation is: s + c + t + c + 70 = 306, which simplifies to 2c = 96, yielding c = 48. From source 4, the expression (b - a) + (m - b) + (n - b) + (54 - a) equals 20 + 20 - 20 + 20. This simplifies to 54 + m + n - 2a - b = 40, and further to 2a + b = 14 + m + n. Rearranging gives 2b = 28 + 2m + 2n - 4a (Equation i). From source 7, b - a = n - b, which means 2b = a + n (Equation ii). Also from source 7, m - b = 54 - a, leading to a + m = 54 + b, and therefore 2b = 2a + 2m - 108 (Equation iii). From source 8, 108 = b + n, so 2b = 216 - 2n (Equation iv). Equating Equations (i) and (ii): 28 + 2m + 2n - 4a = 2a + 2m - 108, simplifying to 6a = 136 + 2n, or 3a = 68 + n (Equation v). Equating Equations (ii) and (iv): 216 - 2n = a + n, which leads to a + 3n = 216, or 3a = 648 - 9n (Equation vi). Equating Equations (v) and (vi): 648 - 9n = 68 + n, resulting in n = 58. Substituting n back gives a = 42, b = 50, and m = 62. The completed table is:

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

Based on the table, Delhi exhibits the highest sales amounts in both 2018 (80) and 2019 (100).

Therefore, the correct option is (A) : Delhi and Delhi.

Answer 2

Let 'a' represent the sales amounts in Apparel departments for Delhi and Kolkata in 2018. Let 'b' represent the sales amounts in Apparel departments for Mumbai, Bengaluru, and Delhi in 2018. Let 'c' represent the sales amounts in Home Decor departments for Mumbai and Kolkata in 2018, with 's' and 't' representing the sales amounts for Delhi and Bengaluru respectively in the same department and year. Sales amounts in Apparel departments for Mumbai and Bengaluru in 2019 are denoted by 'm' and 'n' respectively. The table is populated 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 the given information, we have s = 80 and t = 60. Also, s + c + t + c + 70 = 306, which simplifies to 2c = 96, so c = 48. From another set of conditions, (b - a)+(m - b)+(n - b)+(54 - a) = 20 + 20 - 20 + 20, which leads to 54 + m + n - 2a - b = 40. Rearranging this gives 2a + b = 14 + m + n. Further equations derived are: 2b = 28 + 2m + 2n - 4a (i); 2b = a + n (ii); 2b = 2a + 2m - 108 (iii); and 2b = 216 - 2n (iv). Equating (i) and (ii) yields 3a = 68 + n (v). Equating (ii) and (iv) results in a + 3n = 216, which can be written as 3a = 648 - 9n (vi). Comparing (v) and (vi), we find n = 58, a = 42, b = 50, and m = 62. The completed table is:

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

The Apparel Department in Mumbai recorded sales of 62 Crore rupees in 2018 and 50 Crore rupees in 2019. The increase in sales from 2018 to 2019 is 62 - 50 = 12.

Therefore, the correct option is (A) : 12.

Answer 3

Let 'a' represent the 2018 Apparel sales in Delhi and Kolkata. Let 'b' represent the 2018 Apparel sales in Mumbai, Bengaluru, and Delhi. Let 'c' represent the 2018 Home Decor sales in Mumbai and Kolkata, with 's' and 't' representing the 2018 Home Decor sales in Delhi and Bengaluru, respectively. The 2019 Apparel sales in Mumbai and Bengaluru are denoted by 'm' and 'n', respectively. The table is populated 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 derived information (6), s = 80 and t = 60. From derived information (5), the equation s + c + t + c + 70 = 306 simplifies to 2c = 96, yielding c = 48. From derived information (4), the expression (b - a) + (m - b) + (n - b) + (54 - a) equals 40, which simplifies to 2a + b = 14 + m + n. This leads to equation (i): 2b = 28 + 2m + 2n - 4a. From derived information (7), b - a = n - b, resulting in equation (ii): 2b = a + n. Also from (7), m - b = 54 - a, leading to 2b = 2a + 2m - 108 as equation (iii). From derived information (8), 108 = b + n, yielding equation (iv): 2b = 216 - 2n. Equating (i) and (ii) yields 28 + 2m + 2n - 4a = a + n, which simplifies to 3a = 68 + n (equation v). Equating (ii) and (iv) gives a + n = 216 - 2n, which simplifies to a + 3n = 216 (equation vi). Equating (v) and (vi) leads to 648 - 9n = 68 + n, resulting in n = 58. Substituting n = 58 into equation (v) gives a = 42. Substituting a = 42 into equation (ii) gives b = 50. Substituting b = 50 and a = 42 into equation (iii) gives m = 62. The completed table is:

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

The Home Decor department in Mumbai shows the highest percentage sales increase from 2018 to 2019. Percentage Increase = \( \frac{72-48}{48}\times100 \) = \( \frac{24}{48}\times100 \) = 50.

The correct option is (B) 50.

Answer 4

Let 'a' represent the sales amounts for the Apparel departments in Delhi and Kolkata for the year 2018. Let 'b' denote the sales amounts for the Apparel departments in Mumbai, Bengaluru, and Delhi for 2018. For Home Decor departments in 2018, let 'c' be the sales for Mumbai and Kolkata, 's' for Delhi, and 't' for Bengaluru. In 2019, let 'm' and 'n' be the sales amounts for the Apparel departments in Mumbai and Bengaluru, respectively. The table structure for sales amounts (in Crore rupees) is presented 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 information item 6, we find that s = 80 and t = 60. From information item 5, the equation s + c + t + c + 70 = 306 simplifies to 2c = 96, resulting in c = 48. From information item 4, the expression (b - a) + (m - b) + (n - b) + (54 - a) equals 20 + 20 - 20 + 20, which simplifies to 54 + m + n - 2a - b = 40. This further reduces to 2a + b = 14 + m + n, and subsequently 2b = 28 + 2m + 2n - 4a (Equation i). From information item 7, b - a = n - b leads to 2b = a + n (Equation ii). Also from item 7, m - b = 54 - a gives a + m = 54 + b, which implies 2b = 2a + 2m - 108 (Equation iii). From information item 8, 108 = b + n, so 2b = 216 - 2n (Equation iv). Equating Equation (i) and Equation (ii) yields 28 + 2m + 2n - 4a = 2a + 2m - 108, which simplifies to 6a = 136 + 2n, or 3a = 68 + n (Equation v). Equating Equation (ii) and Equation (iv) gives 216 - 2n = a + n, leading to a + 3n = 216, or 3a = 648 - 9n (Equation vi). Equating Equation (v) and Equation (vi) results in 648 - 9n = 68 + n, from which we find n = 58. Substituting n = 58 into Equation (v) gives a = 42. Substituting a = 42 and n = 58 into Equation (ii) gives b = 50. Substituting b = 50 and a = 42 into the relation a + m = 54 + b yields m = 62. The completed table with all sales amounts (in Crore rupees) is 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

Based on the final table, the total sales amounts for each Departmental Store in 2019 are: Delhi = 50 + 98 + 100 = 248; Mumbai = 62 + 102 + 72 = 236; Bengaluru = 58 + 70 + 80 = 208; Kolkata = 54 + 100 + 54 = 208. The total sales amount for all stores in 2019 is 248 + 236 + 208 + 208 = 900.

Therefore, the correct option is (D) 900.