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GATE CSE 2021 Set 2 Q9: Ratio of selling prices from units, cost and tax data

Question

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 3 was ₹1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 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 2 to the selling price in Year 3 is ________.

Bar chart for Years 1, 2, 3: number of units (hatched bars) 100, 200, 300 and net profit in rupees (black bars) 240, 296, 210
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Answer: A (official GATE 2021 final answer key)

Concept used: Net profit = SP − cost − tax, with tax a percentage of SP.

First step: Year 2: cost =200×2=400= 200 \times 2 = 400, so 0.87 SP2=296+4000.87\,SP_2 = 296 + 400; Year 3: cost =300= 300, so 0.85 SP3=210+3000.85\,SP_3 = 210 + 300.

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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