A shopkeeper sells 20 Timex watches and earns a profit equal to the selling price of 4 Timex watches. What is his profit percentage on the watches?

Introduction / Context:
This question uses a compact way of describing profit: the shopkeeper's total profit on selling 20 watches is equal to the selling price of 4 watches. Instead of giving cost prices and selling prices directly, the relationship is described verbally. We need to translate this into an algebraic equation and then calculate the profit percentage. It is a standard type in profit and loss, involving ratios and proportional reasoning.

Given Data / Assumptions:

• Total number of watches sold = 20.
• Let the selling price of one Timex watch be S.
• Let the cost price of one Timex watch be C.
• Total selling price of 20 watches = 20S.
• Total cost price of 20 watches = 20C.
• Total profit on 20 watches = 20S − 20C.
• We are told that total profit equals the selling price of 4 watches, that is 4S.

Concept / Approach:
We equate the total profit to 4S. Then we solve for the ratio between selling price and cost price of a single watch, S:C. Once S is expressed as a multiple of C, we can compute the profit percentage as (S − C)/C * 100. The values of S and C themselves are not needed; only their ratio matters for percentage profit.

Step-by-Step Solution:
Given: 20S − 20C = 4S.Rearrange: 20S − 4S = 20C.So, 16S = 20C.Divide both sides by 4: 4S = 5C.Therefore, S = (5/4) * C.Profit per watch = S − C = (5/4)C − C = (1/4)C.Profit percentage = (Profit per watch / C) * 100 = (1/4) * 100 = 25%.

Verification / Alternative check:
Assume C = Rs. 4 per watch.Then S = (5/4) * 4 = Rs. 5 per watch.Total cost for 20 watches = 20 * 4 = Rs. 80.Total selling price for 20 watches = 20 * 5 = Rs. 100.Total profit = 100 − 80 = Rs. 20, which equals the selling price of 4 watches (4 * 5 = Rs. 20).Thus the assumption and calculation are confirmed.

Why Other Options Are Wrong:
A profit of 20% would imply S = 1.2C, which does not satisfy the condition that 20S − 20C equals 4S.30% and 50% also yield different ratios and fail to make total profit equal to 4S.Only 25% matches the required relationship between total profit and selling price.

Common Pitfalls:
A common mistake is to interpret the profit equal to the cost price of 4 watches instead of selling price of 4 watches.Another pitfall is to divide the profit of 4S by 20 directly without converting to a relationship between S and C.Students sometimes try to guess a percentage instead of setting up the algebraic equation, which can easily lead to incorrect answers.

Final Answer:
The profit percentage earned by the shopkeeper is 25 percent.