Q9. 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
________.
A) 4:3
(B) 1:1
(C) 3:4
(D) 1:2
The bar graph shows units sold and net profits for a product across three years, with specific cost relationships and tax rates provided. The task requires finding the ratio of total selling price in Year 2 to Year 3.
Graph Data Extraction
- Units sold: Year 1 = 300, Year 2 = 200, Year 3 = 210
- Net profits: Year 1 = 100 (light bar), Year 2 = 296 (dark bar), Year 3 = 210 (dark bar)
- Cost per unit: Year 3 (C3) = ₹1, Year 2 (C2) = ₹2 (double C3), Year 1 (C1) = ₹3 (triple C3)
- Taxes on selling price (SP): Year 1 = 10%, Year 2 = 13%, Year 3 = 15%
Profit Formula Application
Net profit = Total SP – (Total cost + Tax)
Total cost = Units × Cost per unit; Tax = Tax rate × Total SP
For Year 2: 296 = SP2 – (200 × 2 + 0.13 × SP2) = SP2 – 400 – 0.13 SP2
0.87 SP2 = 696 → SP2 = 696 / 0.87 = ₹800
For Year 3: 210 = SP3 – (210 × 1 + 0.15 × SP3) = SP3 – 210 – 0.15 SP3
0.85 SP3 = 420 → SP3 = 420 / 0.85 = ₹600
Ratio SP2 : SP3 = 800 : 600 = 4 : 3
Option Analysis
(A) 3:4 Incorrect; reverses the ratio (would imply SP2 < SP3, but Year 2 profit per unit higher despite fewer units)
(B) 1:1 Incorrect; ignores higher Year 2 profit (296 vs. 210) and tax/cost differences yielding SP2 > SP3
(C) 3:4 Incorrect; same reversal as (A), mismatched to calculations
(D) 2:1 Incorrect; overstates SP2 advantage (actual 800/600 = 1.33, not 2)
Introduction (with Key Phrase)
In CSIR NET Life Sciences Part A and GATE exams, data interpretation questions like “units sold net profit ratio Year 2 Year 3” test graph reading, profit formulas, and ratio calculations. This bar graph problem involves 200 units in Year 2 (profit ₹296), 210 in Year 3 (profit ₹210), with costs ₹2 and ₹1 per unit, and taxes 13% vs. 15%. Master it for quantitative aptitude success.
Why This Question Matters for CSIR NET
- Bar graphs in CSIR NET Part A (15-20% weightage) combine biology context with math skills like percentages and ratios
- Practice identifies trends: Year 2 higher profit despite fewer units due to doubled cost efficiency
- Key phrase “units sold net profit ratio Year 2 Year 3” appears in GATE CSE 2021 and similar exams
Step-by-Step Solution
- Extract values from shaded bars: Units Year 2=200, Profit=296; Year 3=210, Profit=210
- Use profit equation: SP(1 – tax%) = Profit + Total cost
- Compute SP2=₹800, SP3=₹600 → Ratio 4:3
| Year | Units | Cost/Unit (₹) | Tax % | Total Cost (₹) | Net Profit (₹) | Total SP (₹) |
|---|---|---|---|---|---|---|
| 2 | 200 | 2 | 13 | 400 | 296 | 800 |
| 3 | 210 | 1 | 15 | 210 | 210 | 600 |
Common Mistakes to Avoid
- Misreading bars (e.g., Year 1 profit=100, not stacked)
- Forgetting taxes on SP, not cost
- Ratio per unit vs. total (question specifies total selling price)
Correct Answer: 4:3 – Always verify tax is on selling price, not cost. Practice similar bar graph questions daily for Part A mastery!
