While purchasing one item costing ₹ 400, I had to pay the sales tax at 7% and on another costing ₹ 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average?

### Concept & Formula This problem requires calculating the weighted average of two percentages. You cannot simply average the two percentages because they are applied to vastly different base amounts (costs). $$ \text{Weighted Average \%} = \frac{\text{Total Tax Paid}}{\text{Total Cost Base}} \times 100 $$ ### Step-by-Step Solution * **Given:** * Cost of item 1 = ₹ 400 * Tax on item 1 = 7% * Cost of item 2 = ₹ 6400 * Tax on item 2 = 9% * **Calculation:** * **Step 1: Calculate the absolute tax for each item.** Tax 1 = 7% of 400 = 28. Tax 2 = 9% of 6400 = 576. * **Step 2: Find the total tax and total cost.** Total Tax Paid = $28 + 576 = 604$. Total Cost = $400 + 6400 = 6800$. * **Step 3: Calculate the overall tax percentage.** Overall Tax % = $\left( \frac{604}{6800} \right) \times 100\%$ $= \frac{604}{68}\%$ Divide both numerator and denominator by 4: $= \frac{151}{17}\%$ * **Step 4: Convert to a mixed fraction.** $151 \div 17 = 8$ with a remainder of 15. So, $\frac{151}{17}\% = 8\frac{15}{17}\%$. ### Exam Strategy & Shortcut Use the weighted average ratio shortcut to save calculation time. The ratio of the costs is $400 : 6400$, which simplifies to $1 : 16$. Apply these weights directly to the tax percentages: $\text{Average} = \frac{(1 \times 7) + (16 \times 9)}{1 + 16}$ $= \frac{7 + 144}{17} = \frac{151}{17} = 8\frac{15}{17}\%$. ### Common Pitfall A very common mistake is finding the simple arithmetic mean of the two tax rates: $\frac{7 + 9}{2} = 8\%$. This completely ignores the proportional weight of the much more expensive ₹ 6400 item, which pulls the true average closer to 9%. ### Final Answer **Therefore, the correct answer is $8\frac{15}{17}\%$.**