EgmatQuantExpert wrote:
e-GMAT Question of the Week #3A store purchased an article at a wholesale price of $75 and sold it at two successive discounts of 20% and 16.67% respectively, making a profit of 33.3% on the whole price of the article. The store sold another similar article at the same price, making a loss of 33.3% on the whole price. If the second article has a mark-up of 200% over its retail selling price, find by what percentage the mark-up price of 2nd article is more than that of 1st article?
A. 50
B. 75
C. 100
D. 125
E. 200
Article 1:
Cost (mentioned as wholesale price) = $75
Profit after 2 successive discounts = 33.33% = \(\frac{1}{3}\) of cost.
So, profit = \(\frac{1}{3} * 75\) = $25
So, article 1 was sold at $100.
What was the price quoted (Marked price) for Article 1 before the discounts?
1st discount 20%. So, its price after 1st discount = 80% of Marked price = 4/5 Marked price
2nd discount 16.67% (same as 1/6) of the price after 1st discount.
So, its price after 2nd discount = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\) of price after 1st discount.
So, final selling price, $100 = \(\frac{4}{5} * \frac{5}{6}\) of Marked price
So, 100 = \(\frac{4}{6}\) of Marked Price
Marked Price of Article 1 = $150. ---- (1)
Article 2: Selling price = $100 (Same as Article 1)
Loss = 33.33% = \(\frac{1}{3}\) of cost.
So, it sold at 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\) of cost = $100.
So, cost of Article 2 = $150
Article 2 had a mark up of 200%.
So, Marked price of Article 2 = 150 + 200% of 150 = $450 --- (2)
Question is how much percentage is (2) more than (1).
$450 is $300 more than $150.
In terms of percentage \(\frac{300}{150}*100\) = 200%
Choice E
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