A sells a scooter priced at ₹ $36000$. He gives a discount of $8\%$ on the first ₹ $20000$ and $5\%$ on the next ₹ $10000$. How much discount can he afford on the remaining ₹ $6000$ if he is to get as much as when $7\%$ discount is allowed on the total?

### Concept & Strategy This problem is about weighted averages and total discount matching. The total monetary discount allowed must remain constant regardless of whether it is calculated as a flat rate on the total amount or as a sum of variable rates on partial amounts. $$ \text{Total Target Discount} = D_1(\text{Part}_1) + D_2(\text{Part}_2) + D_3(\text{Part}_3) $$ ### Step-by-Step Solution * **Given:** * Total Price = ₹ $36000$ * Target overall discount = $7\%$ on ₹ $36000$ * Discount 1 = $8\%$ on ₹ $20000$ * Discount 2 = $5\%$ on ₹ $10000$ * Remaining amount = ₹ $6000$ * **Calculation:** * First, calculate the total target discount amount: $7\%$ of $36000 = \frac{7}{100} \times 36000 = ₹ 2520$. * Next, calculate the discount already given on the first part: $8\%$ of $20000 = \frac{8}{100} \times 20000 = ₹ 1600$. * Calculate the discount given on the second part: $5\%$ of $10000 = \frac{5}{100} \times 10000 = ₹ 500$. * Find the total discount given so far: $1600 + 500 = ₹ 2100$. * Determine the remaining discount needed to hit the target: $2520 - 2100 = ₹ 420$. * Find what percentage this remaining discount is of the remaining ₹ $6000$: $\text{Discount \%} = \left(\frac{420}{6000}\right) \times 100 = 7\%$. ### Exam Strategy & Shortcut You can use the method of deviation (weighted averages). The total needs to balance out to a $7\%$ average. First ₹ $20,000$ (Weight 20) is at $8\%$ ($+1\%$ deviation). Total surplus = $20 \times 1 = +20$. Next ₹ $10,000$ (Weight 10) is at $5\%$ ($-2\%$ deviation). Total deficit = $10 \times (-2) = -20$. The deviations cancel each other out ($+20 - 20 = 0$). Since the deviation is currently zero, the remaining part (Weight 6) must exactly match the target average of $7\%$ to keep the overall average at $7\%$. ### Common Pitfall A common mistake is attempting to average the percentages directly (e.g., $(8+5+x)/3 = 7$) without accounting for the fact that they apply to different principal amounts. Always use absolute monetary values or weighted averages. ### Final Answer Therefore, the correct answer is **7%**.