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?

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	-	-	-	-	-	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	-	100	-	72	-	80	-	54

Clue 1 says,

sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.

Let that be "x".

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	y	y	-	y	-	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	-	100	-	72	-	80	-	54

Clue 2 says,

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.

Let the sales amount in Mumbai and Bengaluru in 2018 and delhi in 2019 be "y".

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	y	y	-	y	-	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	-	100	z	72	-	80	z	54

Clue 3 says,

sales amounts in the HomeDecor departments were the same for Mumbai and Kolkata in 2018.

Let that be "z".

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 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

Clue 6 says,

sales amounts in the HomeDecor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.

=> Home decor in deli in 2018 = $100 - 20 = 80$

and, in Bengaluru = $80 - 20 = 60$

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	y	y	-	y	-	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	48	72	60	80	48	54

Clue 5 says,

total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.

Now, total sales amount of homedecor in 2018 = $80 + z+60+z = 140 + 2z$

and, total sales of homedecor in 2019 = $100+72+80+54 = 306$

Now, $140 + 2z + 70 = 306$

=> z = $48$

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	y	y	54 + y - x	y	2y - x	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	48	72	60	80	48	54

According to clue 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.

=> Sales amount in Delhi has increased by ( y - x)

=> sales amount in Bengaluru will also increase by (y-x)

Therefore, Bengaluru 2019 = y + (y - x) = 2y - x

Similarly, Increase in sales amount in Kolkata = 54 - x

=> In Mumbai in 2019 it will be y + (54 - x)

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	y	y	54 + y - x	y	2y - x	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	48	72	60	80	48	54

Clue 8,

The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.

Since Sales for Delhi, Kolkata and Bangalore in 2019 form an AP, the following must be true:

Kolkata (2019) - Delhi (2019) = Bengaluru (2019) - Kolkata (2019)

54 - Y = (2Y - X) - 54

108 = 3Y - X …........................(Equation 1)

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 2019
Apparels	x	y	y	54 + y - x	y	2y - x	x	54
Electronics	78	98	82	102	90	70	80	100
HomeDecor	80	100	48	72	60	80	48	54

Clue 4 says,

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.

=> $(98 + 102 + 70 + 100) - (78 + 82 + 90 + 80) = (Y + 54 + Y - X + 2Y - X + 54) - (X + Y + Y + X)$

=> $370 - 330 = (108 + 4Y - 2X) - (2Y + 2X)$

=> $40 = 108 + 2Y - 4X$

=> $4X - 2Y = 68…$........................(Equation 2)

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 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

Solve equations 1 and 2

4X - 2Y= 68

12Y - 4X = 432

10Y = 500

Y = 50

X = 42

Category	Delhi 2018	Delhi 2019	Mumbai 2018	Mumbai 2019	Bengaluru 2018	Bengaluru 2019	Kolkata 2018	Kolkata 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

The max % increase is 50% for Mumbai in Home décor dept.