A wholesale dealer allows a discount of 20 percent on the marked price to the retailer. The retailer then sells the article at 5 percent below the marked price to the final customer. If the customer pays Rs. 19 for the article, what is the retailer's profit in rupees on that article?

Introduction / Context:
This question explores the profit made by a retailer who buys goods from a wholesaler at a discount on the marked price and then sells the same goods at another price to the final customer. The goal is to identify the retailer's cost price and selling price, and then compute the profit in rupees.

Given Data / Assumptions:

• Marked price of the article = M (unknown).
• Wholesale dealer gives retailer a discount of 20 percent on M.
• Retailer sells to customer at 5 percent below M, that is at 95 percent of M.
• The customer pays Rs. 19 for the article, which is this final selling price.
• We must find the retailer's profit in rupees.

Concept / Approach:
The retailer's cost price is the price he pays to the wholesaler, which is the marked price less 20 percent. His selling price is the price at which he sells to the customer, which is 5 percent less than the marked price. By expressing both cost price and selling price in terms of M, and then using the fact that the selling price equals Rs. 19, we can determine M and hence compute the profit as selling price minus cost price.

Step-by-Step Solution:
Let the marked price be M rupees. Retailer buys from wholesaler at 20 percent discount: cost price for retailer = M * (1 - 20 / 100) = 0.80 * M. Retailer sells to customer at 5 percent below marked price: selling price = M * (1 - 5 / 100) = 0.95 * M. Given final selling price to customer = 19 rupees. So 0.95 * M = 19, hence M = 19 / 0.95 = 20 rupees. Retailer's cost price = 0.80 * 20 = 16 rupees. Retailer's selling price = 19 rupees. Retailer's profit = selling price - cost price = 19 - 16 = 3 rupees.

Verification / Alternative check:
To check, we can recalculate from the determined marked price. Marked price M = 20 rupees. The wholesaler gives 20 percent discount, so the retailer pays 20 * 0.80 = 16 rupees. Retailer charges the customer 5 percent less than 20, that is 20 * 0.95 = 19 rupees. The customer indeed pays 19 and retailer gains 3 rupees, consistent with the information given.

Why Other Options Are Wrong:
Rs. 4 and Rs. 5: These profits would require different relationships between marked price and discounts, which do not match the actual calculations. Rs. 1: This underestimates the profit and arises from miscalculating the retailer's cost or the customer's payment. Only Rs. 3 is consistent with the computed cost and selling prices.

Common Pitfalls:
Some candidates confuse the discount given by the wholesaler with the discount given by the retailer and mistakenly combine them directly. Others misidentify the base on which each percentage is applied. The wholesaler's discount is on marked price when selling to the retailer, and the retailer's discount is also on marked price when selling to the customer. Keeping these roles clear is essential for correct calculation.

Final Answer:
The retailer makes a profit of Rs. 3 on the article.