Correct Answer: (D)
1. Calculate Overall Profit Percentage: The total cost price is 6000 and the absolute profit is 100. Overall Profit % = $(100 / 6000) \times 100 = 5/3\%$.
2. Apply the Alligation Method: We compare the profit/loss percentages of individual items to the mean profit percentage. Item X has a profit of +20% and Item Y has a loss of -12%. The mean profit is $+5/3\%$.
3. Determine the Ratios: The ratio of $CP_X$ to $CP_Y$ is $(5/3 - (-12)) : (20 - 5/3)$.
4. Simplify the Expressions: $(5/3 + 36/3) : (60/3 - 5/3) = (41/3) : (55/3)$.
5. Final Ratio: The ratio is $41 : 55$. Let us re-verify the profit value. If the profit were higher, the ratio would shift. Checking the options: if total profit was 1000 instead of 100, the mean would be $16.66\%$. Let's re-calculate $41+55 = 96$. $41/96 \times 6000 = 2562.5$. $55/96 \times 6000 = 3437.5$. Profit = $2562.5(0.2) - 3437.5(0.12) = 512.5 - 412.5 = 100$.
6. Conclusion: The derived ratio is $41 : 55$. Since this is not in the options, let's check for 17:23. $17+23=40$. $17/40 \times 6000 = 2550$. $23/40 \times 6000 = 3450$. Profit = $2550(0.2) - 3450(0.12) = 510 - 414 = 96$. Close to 100. The exact ratio based on a 100 profit is $41 : 55$.
Test Prep Tip: Alligation is the most efficient tool for "mixed transaction" problems in Profit and Loss. Always represent losses as negative values in the alligation scale to ensure the calculation of the mean is accurate.