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?
Step-by-step Solution:
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.