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A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. TheΒ sales are categorized by its three departments - β€˜Apparel’, β€˜Electronics’, and β€˜Home DΓ©cor’. AnΒ Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts forΒ 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 inΒ 2018.
2. The sales amounts in the Apparel departments were the same for Mumbai and BengaluruΒ in 2018. This sales amount matched the sales amount in the Apparel department for Delhi inΒ 2019.
3. The sales amounts in the Home DΓ©cor departments were the same for Mumbai and KolkataΒ in 2018.
4. The sum of the sales amounts of four Electronics departments increased by the sameΒ amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.
5. The total sales amounts of the four Home DΓ©cor departments increased by Rs 70 CroresΒ from 2018 to 2019.
6. The sales amounts in the Home DΓ©cor departments of Delhi and Bengaluru each increasedΒ by Rs 20 Crores from 2018 to 2019.
7. The sales amounts in the Apparel departments of Delhi and Bengaluru each increased byΒ the same amount in 2019 from 2018. The sales amounts in the Apparel departments ofΒ 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 2019Β followed an Arithmetic Progression.

Question 4

What was the total sales amount, in Crore Rupees, in 2019 for the chain ofΒ departmental stores?

From 1,Β LetΒ sales amounts in the Apparel departments for Delhi and Kolkata in 2018 be a.

From 2,Β Let sales amounts in the Apparel departments for Mumbai and Bengaluru in 2018 and for DelhiΒ beΒ b.

From 3,Β let the sales amounts in the Home DΓ©cor departments for Mumbai and Kolkata in 2018 beΒ cΒ and that of Delhi and Bengaluru beΒ sΒ andΒ tΒ respectively.

Let theΒ Let sales amounts in the Apparel departments for Mumbai and Bengaluru in 2019 beΒ mΒ andΒ nΒ respectuvely.

The table looks like:

image


From 6,Β s=80 and t=60.
From 5, s+c+t+c+70=306 => 2c=96 =>Β 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) & (iii), 28+2m+2n-4a=2a+2m-108 => 6a=136+2n => 3a=68+n...(v)

from (ii) & (iv), 216-2n=a+n => a+3n=216=> 3a=648-9n...(vi)

from (v) & (vi), 648-9n=68+n => n=58 => a=42 => b=50 => m=62.

The final table looks like this

WhatsApp Image 2020-12-25 at 11

.'.Β total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores =900 cr.Β 

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