A retailer marks her goods in such a way that the profit made by selli

Question

A retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles. What is the percentage of profit made by the retailer?

A) 66.67%
B) 33.33%
C) 40%
D) 25%
E) 20%

Source:4gmat

eshan429 · Answer

We know,  Selling Price (SP) = Cost (C) + Profit (P)

Also,  Percentage Profit = \frac{{SP - C}}{C} = \frac{P}{C}

Now, the question tells us  50 * P = 20 * SP

or  50 * P = 20 * (C + P)

or  30 * P = 20 * C

or  \frac{P}{C} = \frac{20}{30} \approx 0.6667 = 66.67%

KarishmaB · Answer

Say, cost price of each article = CP and selling price of each = SP

We are given:

(SP - CP)*50 = 20*SP

30*SP = 50*CP

\frac{SP}{CP} = \frac{5}{3}

\frac{(SP - CP)}{CP} = \frac{(5 - 3)}{3} = \frac{2}{3}  (Subtracting 1 from both sides)

Profit% = \frac{(SP - CP)}{CP} * 100 = \frac{2}{3} * 100 = 66.7%

PareshGmat · Answer

I recall this problem already present in the forums......

Let Cost Price = x

Profit = y

Selling Price = x+y

50y = 20(x+y)

30y = 20x

Percentage Profit  = \frac{y}{x} * 100 = \frac{20}{30} * 100 = 66.667%

Answer = A

patronumbeagle · Answer

hi  KarishmaB

Are we assuming that c ost and selling price is the same for all the goods?

The wording "A retailer marks her goods in such a way" Doesnt imply a differenciate selling price for the articles?

KarishmaB · Answer

Yes. the context of the question implies that cost price of all articles is identical and so is the selling price. Otherwise there is no way to find the profit made by retailer. Normally, GMAT official questions would add a word such as "identical" - that the goods are identical. So something on the lines of "50 identical widgets" etc. Even if it just says "50 widgets' we are to assume that they are the same, especially in Problem solving questions since we need an answer.

hr1212 · Answer

P = SP - CP

We are given,

50P = 20SP
50*(SP - CP) = 20SP
SP = CP*5/3

P = SP - CP = CP*5/3 - CP = CP*2/3

Profit percentage = (100*Profit)/Cost Price = 100*P/CP = 100*(CP*2/3)/CP = 200/3 = 66.67%

IMO: A

PietroCavallo · Answer

Just wanted to point out that asking for profit percentage implies profit margin = Profit/ Revenues 
in this case what is really asked is the mark up on the cost : Profit / Cost

A retailer marks her goods in such a way that the profit made by selli

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