A shopkeeper sells 9 Rolex watches and earns a total profit equal to the selling price of 4 Rolex watches. What is his profit percentage on each watch?

Introduction / Context:
This question examines the link between total profit on multiple items and profit percentage on each item when all are sold at the same price. Instead of giving the cost or selling prices directly, it describes profit in terms of the selling price of some of the items. This type of question is common in aptitude exams because it tests your ability to set up equations based on a word description.

Given Data / Assumptions:

• 9 Rolex watches are sold.
• Total profit earned is equal to the selling price of 4 Rolex watches.
• All watches are identical and sold at the same selling price.
• We need to find the profit percentage on each watch.

Concept / Approach:
Let cost price per watch be C and selling price per watch be S. Total cost for 9 watches is 9C, and total selling price is 9S. The total profit is 9S - 9C. The question states that this total profit equals the selling price of 4 watches, that is 4S. This gives an equation involving S and C. Once we determine S in terms of C, we can compute profit percentage as (S - C) / C * 100.

Step-by-Step Solution:
Let cost price of one watch be C and selling price of one watch be S.Total profit on 9 watches = 9S - 9C.Given this profit equals the selling price of 4 watches, so 9S - 9C = 4S.Rearrange: 9S - 4S = 9C, so 5S = 9C.Therefore S = 9C / 5 = 1.8C.Profit per watch = S - C = 1.8C - C = 0.8C.Profit percentage = (0.8C / C) * 100 = 80%.

Verification / Alternative check:
Take an easy value, for example C = Rs 100. Then S = 1.8 * 100 = Rs 180. Total cost for 9 watches = 9 * 100 = Rs 900. Total selling price = 9 * 180 = Rs 1620. Profit = 1620 - 900 = Rs 720. Selling price of 4 watches = 4 * 180 = Rs 720, which matches the given condition, confirming our calculations. Profit percentage per watch is (180 - 100) / 100 * 100 = 80% as derived.

Why Other Options Are Wrong:
44.4 percent, 88.8 percent or 8.8 percent are not compatible with the relationship 9S - 9C = 4S. Using any of those values leads to different equations between S and C and fails to reproduce the given profit description. Only 80 percent satisfies the exact condition described in the problem.

Common Pitfalls:
Some learners divide 4 by 9 and directly treat it as the profit percentage, which is incorrect. Others may confuse the total profit with profit per watch and set up an incorrect equation. Carefully defining variables and writing a clear total profit equation helps avoid such mistakes.

Final Answer:
The profit percentage on each Rolex watch is 80 percent.