9.8.4 Bar Graph: GATE CSE 2021 Set 2 | GA Question: 6 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 F, 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 30%, 10%, and 10% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes. The ratio of the selling price in Year 2 to the selling price in Year 3 is: A. 4 : 3 B. 1 : 1 C. 3 : 4 D. 1 : 2
GATE 2021 · General Aptitude · Bar Graph · medium
Answer: The ratio of selling price in Year 2 to Year 3 = 4 : 3. Answer: A. 4 : 3.
- Set up cost and tax for Years 2 and 3: Cost per unit: Year 3 = F, Year 2 = 2F (since Year 3 is half Year 2). Tax rate = 10% of SP for both Years 2 and 3.
- Express net profit condition and derive SP formula: Net Profit % (NP%) from bar graph: Year 2 ≈ 0% (breakeven), Year 3 ≈ 50% on cost. SP2 = 2F*(1+0)/0.9 = 2F/0.9 = 20F/9. SP3 = F*(1+0.5)/0.9 = 1.5F/0.9 = 15F/9.
- Compute ratio SP2 : SP3: SP2/SP3 = (2F/0.9) / (1.5F/0.9) = 2F / 1.5F = 2/1.5 = 4/3. Therefore SP2 : SP3 = 4 : 3.