A shopkeeper sells 13 Titan watches and earns a total profit equal to the selling price of 3 Titan watches. What is the shopkeeper's profit percentage?

Introduction / Context:
This problem mirrors the previous one, but with different numbers. It again tests your ability to interpret profit information in terms of the selling price of some of the items and to convert that relationship into a profit percentage on cost price.

Given Data / Assumptions:

• Total watches sold = 13 Titan watches.
• Total profit equals the selling price of 3 watches.
• All watches have the same cost price and selling price per piece.
• We need to find the profit percentage on cost price.

Concept / Approach:
Let S be selling price per watch and C be cost price per watch. Total selling price for 13 watches is 13S, and total cost is 13C. Profit is 13S - 13C and is given to be equal to 3S. Equating these gives a linear equation relating S and C. From that equation, we determine the profit per watch and then the profit percentage on cost price.

Step-by-Step Solution:
Let S = selling price per watch and C = cost price per watch. Total SP for 13 watches = 13S. Total CP for 13 watches = 13C. Profit = 13S - 13C. Given profit = 3S, so 13S - 13C = 3S. Rearrange: 13S - 3S = 13C → 10S = 13C. Thus C = (10/13)S. Profit per watch = S - C = S - (10/13)S = (3/13)S. Profit percentage on cost = [(S - C) / C] * 100 = [(3/13)S / (10/13)S] * 100 = (3/10) * 100 = 30%.

Verification / Alternative check:
Assume S = Rs 13. Then C = (10/13) * 13 = Rs 10. Profit per watch = 13 - 10 = Rs 3. Total profit on 13 watches = 13 * 3 = Rs 39. Selling price of 3 watches = 3 * 13 = Rs 39, which satisfies the condition. Profit percentage = (3 / 10) * 100 = 30%, confirming the answer.

Why Other Options Are Wrong:
23 percent, 46 percent, and 16 percent arise from possible misoperations with 10 and 13. However only 30 percent follows from the correct ratio C = (10/13)S and the resulting profit per watch.

Common Pitfalls:
Some candidates misread the statement and think profit equals cost price of 3 watches instead of selling price, which changes the equation. Others divide by the wrong number or compute profit percentage on selling price instead of cost price.

Final Answer:
The shopkeeper's profit percentage is 30 percent.