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Official PYQ · 2021Set 2 · Q9MCQ2 marks

GATE CS 2021 Set 2 Q9 — General Aptitude

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The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 33 was ₹  1\;1, which was half the cost/unit in Year 22. The cost/unit in Year 33 was one-third of the cost/unit in Year 11. Taxes were paid on the selling price at 10%10 \%, 13%13 \%, and 15%15 \% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 22 to the selling price in Year 33 is _________.

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Answer: A

From the given problem statement, we first determine the cost per unit (CC) for each year:

  • Cost per unit in Year 3 (C3C_3) = ₹ 11
  • Cost per unit in Year 2 (C2C_2) = 2×C32 \times C_3 = ₹ 22
  • Cost per unit in Year 1 (C1C_1) = 3×C33 \times C_3 = ₹ 33

From the bar graph, we obtain the number of units sold and the total net profit for Year 2 and Year 3:

  • Year 2: Units sold = 200200, Total Net Profit = ₹ 296296
  • Year 3: Units sold = 300300, Total Net Profit = ₹ 465465

Let S2S_2 and S3S_3 be the selling prices per unit in Year 2 and Year 3 respectively.

For Year 2:

Net Profit per unit=296200=1.48\text{Net Profit per unit} = \frac{296}{200} = 1.48 S2−(C2+0.13S2)=1.48  ⟹  0.87S2−2=1.48  ⟹  0.87S2=3.48  ⟹  S2=4S_2 - (C_2 + 0.13 S_2) = 1.48 \implies 0.87 S_2 - 2 = 1.48 \implies 0.87 S_2 = 3.48 \implies S_2 = 4

For Year 3:

Net Profit per unit=465300=1.55\text{Net Profit per unit} = \frac{465}{300} = 1.55 S3−(C3+0.15S3)=1.55  ⟹  0.85S3−1=1.55  ⟹  0.85S3=2.55  ⟹  S3=3S_3 - (C_3 + 0.15 S_3) = 1.55 \implies 0.85 S_3 - 1 = 1.55 \implies 0.85 S_3 = 2.55 \implies S_3 = 3

Thus, the ratio of the selling price in Year 2 to that in Year 3 is:

S2S3=43  ⟹  4:3\frac{S_2}{S_3} = \frac{4}{3} \implies 4:3

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