A shopkeeper sells 22 pairs of Skechers shoes and earns a total profit equal to the selling price of 6 pairs of the same shoes. What is his profit percentage on each pair?

Introduction / Context:
This question is about interpreting a verbal description of profit in terms of number of items sold. The shopkeeper's total profit from selling 22 pairs of shoes is equal to the selling price of 6 pairs. From this information, you must derive the profit percentage per pair. This style of question is common in profit and loss topics and emphasizes translation of words into algebraic equations.

Given Data / Assumptions:

• Number of pairs sold = 22.
• Total profit from selling these 22 pairs equals the selling price of 6 pairs.
• Let SP be the selling price per pair.
• Let CP be the cost price per pair.
• We assume all pairs are identical and sold at the same price.

Concept / Approach:
We translate the condition into an equation:

• Total selling price for 22 pairs = 22 * SP.
• Total cost price for 22 pairs = 22 * CP.
• Total profit = 22 * SP - 22 * CP.
• Given: Total profit = selling price of 6 pairs = 6 * SP.

We solve for the ratio SP / CP and then compute profit percentage = ((SP - CP) / CP) * 100.

Step-by-Step Solution:
Step 1: Let SP = selling price per pair, CP = cost price per pair. Step 2: Total SP for 22 pairs = 22 * SP. Step 3: Total CP for 22 pairs = 22 * CP. Step 4: Total profit = 22 * SP - 22 * CP. Step 5: Given condition: total profit = selling price of 6 pairs = 6 * SP. Step 6: So 22 * SP - 22 * CP = 6 * SP. Step 7: Rearrange: 22SP - 6SP = 22CP. Step 8: 16SP = 22CP. Step 9: Divide both sides by 16CP: SP / CP = 22 / 16 = 11 / 8. Step 10: Profit per pair = SP - CP = (11 / 8)CP - CP = (3 / 8)CP. Step 11: Profit percentage = (Profit / CP) * 100 = (3 / 8) * 100 = 37.5%.

Verification / Alternative check:
Assign a simple numerical CP, for example CP = Rs 8:

• Then SP = (11 / 8) * 8 = Rs 11.
• Profit per pair = 11 - 8 = Rs 3.
• Profit percentage = 3 / 8 * 100 = 37.5%.
• Total profit on 22 pairs = 22 * 3 = Rs 66.
• Selling price of 6 pairs = 6 * 11 = Rs 66.

The total profit equals the selling price of 6 pairs, matching the given condition and confirming that the profit percentage is correct.

Why Other Options Are Wrong:
27.2 percent, 54.4 percent, and 16.9 percent do not correspond to SP / CP = 11 / 8. If any of these percentages were used, the profit from 22 pairs would not exactly equal the selling price of 6 pairs. Only 37.5 percent yields the exact algebraic match to the problem statement.

Common Pitfalls:
A common mistake is to misinterpret the phrase "profit equal to the selling price of 6 pairs" as meaning the profit percentage is 6 / 22 of something, which is incorrect. Another error is to set equations based on per pair values incorrectly, forgetting to multiply by the number of pairs. Always translate the given condition into a precise mathematical equation using total cost and total selling price for all items sold.

Final Answer:
The shopkeeper's profit percentage on each pair of Skechers shoes is 37.5 percent.