Direction: Study the following information carefully and answer the questions. The following pie chart shows the distribution of the number of laptops sold by five stores. Conditions: I. The total number of laptops sold by all the five stores (A, B, C, D and E) taken together is 7200. II. $(19z - 4y) = 42$ III. $z^2 + 2z - 224 = 0$ Note: The values given in the above given pie chart in the form of degree or percentage form cannot be negative. If the MRP of each laptop of store A is ₹68000 and $\left(\frac{5}{6}\right)$ of the total number of laptops sold by store A were sold on MRP and remaining were sold at '$a$'% discount, then find out the value of '$a$'. It is assumed that the total amount collected by store A by selling the laptops is ₹122204160.

### Concept & Profit, Loss and Discounts The total revenue is the sum of the items sold at full MRP and the items sold at a discounted price. $$ \text{Total Revenue} = (\text{Qty}_1 \times \text{MRP}) + (\text{Qty}_2 \times \text{MRP} \times (1 - \text{Discount})) $$ ### Step-by-Step Solution * **Given:** Store A's pie chart share is 26%. Total laptops = 7200. * **Calculation:** Laptops sold by Store A = $0.26 \times 7200 = 1872$. * Laptops sold at MRP ($\frac{5}{6}$ of total) = $\frac{5}{6} \times 1872 = 1560$. * Laptops sold at discount ($\frac{1}{6}$ of total) = $1872 - 1560 = 312$. * **Deduction:** Total collected = ₹122,204,160. * Revenue from MRP laptops = $1560 \times 68000 = 106,080,000$. * Revenue from discounted laptops = Total - Revenue from MRP = $122,204,160 - 106,080,000 = 16,124,160$. * Discounted price per laptop = $\frac{16,124,160}{312} = 51680$. * The MRP was 68000, so the absolute discount amount = $68000 - 51680 = 16320$. * Discount percentage '$a$' = $(\frac{16320}{68000}) \times 100 = 24\%$. ### Exam Strategy & Shortcut To handle large numbers, simplify by working out the revenue components sequentially. Finding the individual discounted selling price (₹51,680) and subtracting it from the base ₹68,000 is computationally safer and much faster than running a massive algebraic equation for '$a$'. ### Common Pitfall Students often make arithmetic errors when dealing with large 8-digit revenue numbers. Keeping calculations organized step-by-step prevents cascading addition/subtraction errors. ### Final Answer Therefore, the correct answer is **24**.