Directions (95-98): Read the following information carefully and answer the given questions. A shopkeeper sold five articles: P, Q, R, S and T. Further partial information in given in table below. | Article | Cost price | % Profit | Marked price | |---|---|---|---| | P | - | 40% | $(10.8b + 3m)$ | | Q | - | - | $(12a - n)$ | | R | - | 20% | - | | S | $(5b - m - n - 48)$ | - | - | | T | $(4a + \frac{m}{2})$ | - | $(13a - \frac{n}{2} + 6)$ | Note: (i) Value of '$n$' is 4 times of larger root of given equation. $K^2 - 32P + 252 = 0$ (ii) Article T is marked up ₹1280 more than its cost price and the difference between marked price and cost price of article T is 28% more than profit earned on article S. (iii) Discount given on article Q is 16.66%, and selling price of S is ₹$(5m + 7n + 4a + 296)$. (iv) Value of '$m$' is twice of missing value in the given sequence. 140, 136, 161, $x$, 329, -200 If the discount given on article T is $(b - a)\%$ and sold at a profit of L%, while the marked price of S is ₹400 less than that of P, and S sold after giving a discount of D%. Find (L% - D%).

### Concept & Profit and Loss Strategy This question requires calculating individual profit and discount percentages for articles T and S using the derived variables $a, b, m, n$. Key formulas: $$Profit\ \% = \frac{SP - CP}{CP} \times 100$$ $$Discount\ \% = \frac{MP - SP}{MP} \times 100$$ ### Step-by-Step Solution **1. Recall Base Variables:** * $a = 150$, $b = 200$, $m = 80$, $n = 72$. * From Note (iii), $SP_S = 5(80) + 7(72) + 4(150) + 296 = 1800$. **2. Analyze Article T (Find L%):** * $CP_T = 4a + \frac{m}{2} = 4(150) + \frac{80}{2} = 600 + 40 = 640$. * $MP_T = 13a - \frac{n}{2} + 6 = 13(150) - \frac{72}{2} + 6 = 1950 - 36 + 6 = 1920$. * Discount on T $= (b - a)\% = (200 - 150)\% = 50\%$. * $SP_T = MP_T \times (1 - 0.5) = 1920 \times 0.5 = 960$. * Profit $= SP_T - CP_T = 960 - 640 = 320$. * Profit% ($L\%$) $= \frac{320}{640} \times 100 = 50\%$. Thus, $L = 50$. **3. Analyze Article S (Find D%):** * $MP_P = 10.8b + 3m = 10.8(200) + 3(80) = 2160 + 240 = 2400$. * Given $MP_S$ is ₹400 less than $MP_P$: $MP_S = 2400 - 400 = 2000$. * Discount on S $= MP_S - SP_S = 2000 - 1800 = 200$. * Discount% ($D\%$) $= \frac{200}{2000} \times 100 = 10\%$. Thus, $D = 10$. **4. Final Calculation:** * We need to find $(L\% - D\%) = 50\% - 10\% = 40\%$. ### Exam Strategy & Shortcut Notice that $SP_T$ ($960$) is exactly halfway between $MP_T$ ($1920$) and $0$, making the discount $50\%$. Since $CP_T$ is $640$, the profit of $320$ is exactly half of $640$, making profit $50\%$. Spotting these halving relationships bypasses the need for the formal percentage formula. ### Common Pitfall Be careful not to mix up the absolute values ($L, D$) with their percentage representations. The question asks for the difference in the calculated percentages. Always cross-check the base (MP for discount, CP for profit). ### Final Answer Therefore, the correct answer is **40%**.