Problem Solving

e-GMAT

A 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

OA E.

-Article purchased at 75 dollar (wholesale price)
-Two successive discount of 20% and 16.67% irrespectively
-On this store article made a profit of 33.3% on whole price
-Second article has mark- up price of 200% over its selling price
-Find the % by which the mark-up price of the second article is more that that of the first article.
Profit of the first article $$=\frac{33.33}{100}\cdot75=25dollar$$
Selling price =75 dollar + 25 dollar = 100 dollar, this selling price is obtained after two successive discount of 20% and 16.67%.
$$Let\ the\ marked\ price\ =\ x$$
$$x\cdot\left(1-\frac{20}{100}\right)\cdot\left(1-\frac{16.67}{100}\right)=100$$
$$x\cdot\frac{4}{5}\cdot\frac{5}{6}=100$$
$$x\cdot\frac{2}{3}=100$$
$$x=100\cdot\frac{3}{2}$$
$$x=150\left(makeup\ price\ of\ the\ first\ article\right)$$

Selling price of Article 2 = 100 dollar
There is a loss of 33.3% on whole price
$$Let\ the\ whole\ price=y$$
$$y\cdot\left(1-\frac{33.3}{100}\right)=100$$
$$y\cdot\frac{2}{3}=100$$
$$y=100\cdot\frac{3}{2}$$
$$y=100\cdot\frac{3}{2}=150$$

Since there is a markup of 200%, hence
$$Mark\ up\ price=150+200\%of\ 150$$
$$=150+300=450\ dollars$$
The % by the whole of the second article is more that the first article,
$$\frac{\left(450-150\right)}{150}\cdot100=\frac{300}{150}\cdot100=200\%$$
$$answer\ is\ Option\ E$$