Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent above the cost price were his articles marked?

A) 100%
B) 80%
C) 75%
D) 66+2/3%
E) 50%

Correct Answer: A

Solution and Explanation:

Approach Solution 1:
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)

Selling price = 20% Discount over M = 0.8*M

Given that, a customer bargains and receives 20 articles for the price of 15 articles--> *a further loss of 25% to the dealer--> BUT a NET PROFIT of 20% over cost price (C)

0.75 * 0.8 * M = 1.2 * C

Hence, M/C = 2/1 = 200%

From Eqn. A , (C + Mark up)/C = 200% --> Markup / C = 100%

Approach Solution 2:
Marked Price = M.P.
Cost Price = C.P.
Selling Price = S.P.
Disc. offered on M.P. = 20%

Bargain Disc. = (5∗100)/20 = 25%

Total Discount on M.P. = -20 - 25 + (20∗25)/100 = -45 + 5 = -40% (Successive Percentage Change)

This means that Total Discount Offered by Dealer on M.P. = 40%
=> S.P. = 0.6 M.P.

Dealer Makes a 20% Profit.
=> S.P. = 1.2 * C.P.

Equating S.P.
=> 0.6 M.P. = 1.2 C.P.
=> M.P. = 2 * C.P.

Therefore, Mark up = 100%

Approach Solution 3:
Let us take Price of 1 article=x
Price of 20 article=20X (This is our Marked Price)

Now after bargain 20 articles are sold at price of 15 articles i.e 15x

A discount of 20% is also applied finally
Final S.P= 15x*0.8(20% discount)
Therefore , SP=12 X

Profit earned =20%
CP*1.2=SP
CP=12x/1.2=>10 X

Now it is asked percentage difference between Marked price(20X) and C.P(10X)

We can see this is a 100% increase.

“A dealer offers a cash discount of 20%. Further, a customer bargains”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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