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 \(\underline{\hspace{1cm}}\).
\includegraphics[width=0.75\linewidth]{image9.png}

• A. $4:3$
• B. $1:1$
• C. $3:4$
• D. $1:2$

Hint:

Always convert profit conditions into equations involving selling price, cost, and tax to avoid conceptual mistakes in data interpretation questions.

Answer 1

The Correct Option is A

Step 1: Extract data from the graph.
Year 2: Units sold $= 200$, Net Profit $= 296$
Year 3: Units sold $= 300$, Net Profit $= 210$

Step 2: Determine cost per unit for each year.
Cost/unit in Year 3 $= ₹1$
Cost/unit in Year 2 $= 2 \times 1 = ₹2$
Cost/unit in Year 1 $= 3 \times 1 = ₹3$

Step 3: Compute total cost.
Total cost (Year 2) $= 200 \times 2 = ₹400$
Total cost (Year 3) $= 300 \times 1 = ₹300$

Step 4: Use net profit formula.
\[ \text{Net Profit} = \text{Selling Price} - (\text{Cost} + \text{Tax}) \] Year 2:
Tax rate $= 13%$
\[ 296 = SP_2 - (400 + 0.13\,SP_2) \] \[ 296 = 0.87\,SP_2 - 400 \] \[ SP_2 = \frac{696}{0.87} = 800 \] Year 3:
Tax rate $= 15%$
\[ 210 = SP_3 - (300 + 0.15\,SP_3) \] \[ 210 = 0.85\,SP_3 - 300 \] \[ SP_3 = \frac{510}{0.85} = 600 \]

Step 5: Find the required ratio.
\[ SP_2 : SP_3 = 800 : 600 = 4 : 3 \]

Final Answer:
\[ \boxed{4:3} \]