CAT 2020 Slot 2 — DILR Question 1
Answer the next 4 questions based on the information given below.
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.
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The following additional information is known.
- The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.
- 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.
- The sales amounts in the HomeDecor departments were the same for Mumbai and Kolkata in 2018.
- 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.
- The total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.
- The sales amounts in the HomeDecor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.
- 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.
- The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic
In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?
Answer & solution
Delhi and Delhi
- B
Mumbai and Mumbai
- C
Bengaluru and Delhi
- D
Mumbai and Delhi
HomeDecor:
The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.
∴ Delhi (2018) = 100 – 20 = 80
Bengaluru (2018) = 80 – 20 = 60
The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.
Let Mumbai (2018) = Kolkata (2018) = a
∴ Data for Home Décor will be as follows
The total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.
∴ (80 + a + 60 + a) + 70 = (100 + 72 + 80 + 54)
⇒ 2a + 210 = 306
⇒ a = 48
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Apparels:
The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.
Let Delhi (2018) = Kolkata (2018) = b
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 Mumbai (2018) = Bengaluru (2018) = Delhi (2019) = c
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.
∴ Bengaluru (2019) = c + (c – b) = 2c – b
Also, Mumbai (2019) = c + (54 - b) = c – b + 54
The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.
∴ Delhi – Kolkata = Kolkata – Bengaluru
⇒ Delhi + Bengaluru = 2 × Kolkata
⇒ c + 2c – b = 2 × 54
3c – b = 108 …(1)
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.
From 2018 to 2019, total increase in apparels sales = Total increase in Electronics sales
∴ [c + (c – b + 54) + (2c - b) + 54] – [b + c + c + b] = [98 + 102 + 70 + 100] – [78 + 82 + 90 + 80]
⇒ [4c – 2b + 108] – [2b + 2c] = 370 – 330
⇒ c – 2b = -34 …(2)
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Solving (1) and (2) we get,
b = 42 and c = 50 …(3)
∴ We can make the following table
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For HomeDecor highest sales in 2018 as well as in 2019 was in Delhi.
Hence, option (a).