Direction: In the following question, three quantities I, II and III are given. Compare quantity I, quantity II and quantity III on its basis. (Only quantity is to be considered) Two equations (a) and (b) are given below: (a) 3x - 4y = 2 (b) x - 2y = 8 Quantity I: Find the value of 'x' by solving both the equations? Quantity II: Find the value of 'y' by solving both the equations? Quantity III: An article is marked up by ₹250 and sold by giving a discount of ₹200 on marked price. If the marked up percent is P%, discount given is Q% and marked price of the article is ₹1000, then find the value of (Q - P)?

### Concept & Algebraic Comparison To compare multiple quantities, solve each independent mathematical problem first. For linear equations, use standard substitution or elimination methods. For profit and loss, use the fundamental formulas linking Cost Price (CP), Marked Price (MP), Markup Percentage, and Discount Percentage. ### Step-by-Step Solution * **Calculate Quantity I & II:** * Equation (a): $3x - 4y = 2$ * Equation (b): $x - 2y = 8 \Rightarrow 2x - 4y = 16$ (multiplying the entire equation by 2) * Subtract the modified equation (b) from (a): $(3x - 2x) - (4y - 4y) = 2 - 16 \Rightarrow x = -14$. * Substitute $x = -14$ into (b): $-14 - 2y = 8 \Rightarrow -2y = 22 \Rightarrow y = -11$. * Therefore, Quantity I = $-14$ and Quantity II = $-11$. * **Calculate Quantity III:** * Given: Marked Price (MP) = $1000$, Discount = $200$, Markup amount = $250$. * Cost Price (CP) = $\text{MP} - \text{Markup amount} = 1000 - 250 = 750$. * Markup percent ($P$) = $(\frac{\text{Markup amount}}{\text{CP}}) \times 100 = (\frac{250}{750}) \times 100 = 33.33\%$. * Discount percent ($Q$) = $(\frac{\text{Discount}}{\text{MP}}) \times 100 = (\frac{200}{1000}) \times 100 = 20\%$. * Value of $(Q - P) = 20 - 33.33 = -13.33$. * Therefore, Quantity III = $-13.33$. * **Comparison:** * We have: I = $-14$, II = $-11$, III = $-13.33$. * Arranging in ascending order: $-14 < -13.33 < -11$. * This translates to: Quantity I < Quantity III < Quantity II, which is equivalently written in descending order as Quantity II > Quantity III > Quantity I. ### Exam Strategy & Shortcut When dealing with simple linear equations, coefficient elimination is typically faster than substitution. For the profit/loss section, remember that markup percentage is strictly calculated on the Cost Price (CP), whereas discount percentage is calculated on the Marked Price (MP). ### Common Pitfall A very common mistake is calculating the markup percentage ($P\%$) on the Marked Price instead of the Cost Price, which would yield an incorrect $25\%$ instead of $33.33\%$, altering the final comparison. ### Final Answer Therefore, the correct answer is **Quantity II > Quantity III > Quantity I**.