A shopkeeper sells 17 Omega watches and earns a total profit equal to the selling price of 7 Omega watches. What is the shopkeeper's profit percentage?

Introduction / Context:
This question involves interpreting a profit statement in terms of total selling price and cost price. The seller sells several identical items and is told that the total profit equals the selling price of a certain number of items. From this relationship, we can deduce the cost price per item and hence the profit percentage.

Given Data / Assumptions:

• Total watches sold = 17 Omega watches.
• Total profit earned equals the selling price of 7 watches.
• All watches are identical with the same cost price and selling price per piece.
• We need to find overall profit percentage.

Concept / Approach:
Let S be the selling price per watch and C be the cost price per watch. Then total selling price for 17 watches is 17S and total cost is 17C. Given that the total profit is equal to selling price of 7 watches, profit = 7S. But profit is also 17S - 17C. Equating 17S - 17C to 7S allows us to find a relationship between S and C and hence compute profit percentage.

Step-by-Step Solution:
Let S = selling price per watch, C = cost price per watch. Total SP for 17 watches = 17S. Total CP for 17 watches = 17C. Profit = total SP - total CP = 17S - 17C. Given profit = 7S, so 17S - 17C = 7S. Rearrange: 17S - 7S = 17C → 10S = 17C. So C = (10/17)S → profit per watch = S - C = S - (10/17)S = (7/17)S. Profit percentage on cost = [(S - C) / C] * 100 = [(7/17)S / (10/17)S] *100 = (7/10)*100 = 70%.

Verification / Alternative check:
Assume S = Rs 17 so that S is a multiple of 17. Then C = (10/17)*17 = Rs 10. Profit per watch = 17 - 10 = Rs 7. For 17 watches, total profit = 17 * 7 = Rs 119. Selling price of 7 watches = 7 * 17 = Rs 119, which matches the given condition. Profit percentage = (7 / 10) * 100 = 70%, confirming the calculation.

Why Other Options Are Wrong:
41.1 percent and 82.2 percent are distractor values that could appear from misinterpreting ratios or dividing incorrectly. 12.2 percent is far too small given that profit equals nearly half of total selling price for the 17 watches.

Common Pitfalls:
A typical mistake is to assume profit is equal to cost price of 7 watches, rather than selling price. Another common error is to solve the equation incorrectly and then compute profit percentage using the wrong base. Careful reading and algebra are essential.

Final Answer:
The shopkeeper's profit percentage is 70 percent.