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 profit% given on article Q is thrice as that of discount %, then find difference between cost price of Q and S.

### Concept & Profit and Loss Strategy Deciphering the base variables from the shared Data Interpretation notes provides the Cost Price of S and Marked Price of Q. We apply the standard fractional relationships for profit and discount to find the Cost Price of Q. $$SP = MP \times (1 - Discount\%)$$ $$CP = \frac{SP}{1 + Profit\%}$$ ### Step-by-Step Solution **1. Recall Base Variables:** * From decoding the initial puzzle (solving the quadratic and number sequence): $n = 72$, $m = 80$, $a = 150$, $b = 200$. * From Note (ii) and (iii), $CP_S$ is found to be $800$. **2. Analyze Article Q:** * $MP_Q = 12a - n = 12(150) - 72 = 1800 - 72 = 1728$. * From Note (iii), Discount on Q $= 16.66\% \approx \frac{1}{6}$. * $SP_Q = MP_Q \times (1 - \frac{1}{6}) = 1728 \times \frac{5}{6} = 288 \times 5 = 1440$. **3. Calculate CP of Q:** * Given Profit% is thrice the Discount%: Profit% $= 3 \times 16.66\% = 50\% = \frac{1}{2}$. * $SP_Q = CP_Q \times (1 + \frac{1}{2}) = 1.5 \times CP_Q$. * $1440 = 1.5 \times CP_Q \implies CP_Q = \frac{1440}{1.5} = 960$. **4. Find the Difference:** * Difference $= CP_Q - CP_S = 960 - 800 = 160$. ### Exam Strategy & Shortcut Recognizing $16.66\%$ as $\frac{1}{6}$ and $50\%$ as $\frac{1}{2}$ is crucial for speed. Instead of complex decimals, use fraction multipliers: $SP = MP \times \frac{5}{6}$ and $CP = SP \times \frac{2}{3}$. This turns the calculation into mental math: $1728 \times \frac{5}{6} = 1440 \implies 1440 \times \frac{2}{3} = 960$. ### Common Pitfall A common mistake is applying the $50\%$ profit calculation as a markdown from the Selling Price (i.e., finding $50\%$ of $1440$ and subtracting). Remember that profit percentage is always based on the Cost Price: $SP = CP \times (1 + P\%)$. ### Final Answer Therefore, the correct answer is **160**.