A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the actual price were his article listed?
Let the Cost Price (CP) of one article be C.
Let the Marked Price (MP) of one article be M.
The dealer makes a profit of 20%, so:
Selling Price (SP) = CP + Profit = C + 0.20C = 1.20C.
The dealer offers a 20% cash discount on the Marked Price.
Selling price of one article = M − 0.20M = 0.80M.
The dealer allows 16 articles for the price of a dozen (12 articles).
Effective Selling Price of 16 articles = 12 × 0.80M = 9.6M.
Cost Price of 16 articles = 16C.
Profit is 20% on the cost of the 16 articles.
9.6M = 16C + (0.20 × 16C)
9.6M = 16C + 3.2C
9.6M = 19.2C
From the equation: M = (19.2C) / 9.6
M = 2C
Percentage above actual price = ((M − C) / C) × 100%
= ((2C − C) / C) × 100%
= (C / C) × 100% = 100%
The article was listed (A) 100% above the actual price.
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