While purchasing one item costing Rs. 400 a buyer has to pay sales tax at 7%, and on another item costing Rs. 6400 the sales tax rate is 9%. Taking both items together, what is the average percentage rate of sales tax paid on the total purchase?

Introduction / Context:
This problem checks understanding of weighted averages with percentages. Instead of simply averaging 7% and 9%, you must consider the different prices of the two items because the higher priced item contributes more to the total tax paid. This idea of a weighted average is very common in percentage and profit and loss questions in aptitude examinations.

Given Data / Assumptions:

Cost of first item = Rs. 400.

Sales tax rate on first item = 7%.

Cost of second item = Rs. 6400.

Sales tax rate on second item = 9%.

We assume tax is calculated on the listed price of each item independently.

Concept / Approach:
The key concept is weighted average percentage. The average tax rate on the combined purchase is:
average tax rate = (total tax paid on both items / total cost of both items) * 100.
We therefore first compute the tax on each item, then add them to get total tax, then divide by the total amount spent on the two items, and finally convert this fraction to a percentage and mixed fraction as required.

Step-by-Step Solution:
Step 1: Tax on first item = 7% of 400.That is (7 / 100) * 400 = Rs. 28.Step 2: Tax on second item = 9% of 6400.That is (9 / 100) * 6400 = Rs. 576.Step 3: Total tax paid = 28 + 576 = Rs. 604.Step 4: Total cost price of both items = 400 + 6400 = Rs. 6800.Step 5: Average tax rate on the whole purchase = (604 / 6800) * 100.Compute 604 / 6800 = 0.0888235 (approximately).Step 6: Convert 0.0888235 to percentage: 0.0888235 * 100 ≈ 8.88235%.Step 7: Express 8.88235% as a mixed fraction; this is exactly 8 15/17%.

Verification / Alternative check:
Notice that the second item is far more expensive and has the higher tax rate of 9%. Therefore the overall average must be closer to 9% than to 7%. The computed value 8 15/17% is indeed closer to 9%, which makes the answer reasonable and consistent with intuition.

Why Other Options Are Wrong:
2 13/17% and 3 2/17% are far too small and would imply extremely low tax relative to total cost, which does not match the given rates.
5 13/12% is more than 6%, which is still too far from the weighted average that should lie between 7% and 9% and close to 9% because of the expensive second item.
8% ignores the different costs and simply feels like a rough guess, not the precise weighted average.

Common Pitfalls:
A common mistake is to calculate the simple average (7% + 9%) / 2 = 8%, which is wrong because it does not account for the fact that the second item costs much more. Another frequent error is to round too aggressively during intermediate steps, which can disturb the exact fraction form. Always compute individual taxes, add them, and then divide by the combined base to get an accurate weighted average.

Final Answer:
The average percentage rate of sales tax on the combined purchase is 8 15/17%.