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A dealer purchased an antique for $240 and then marked up the price of

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nislam
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A dealer purchased an antique for $240 and then marked up the price of [#permalink] New post   25 May 2022, 02:58
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A dealer purchased an antique for $240 and then marked up the price of the antique by 40 percent of the selling price. If the merchant subsequently discounted the antique by 20% of the selling price and so the antique, then what was the merchant's gross profit as a percent of his original purchase price?

(A) 25 %

(B) 33 \(\frac{1}{2 }\)%

(C) 35 %

(D) 37.5 %

(C) 40 %
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nislam
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Re: A dealer purchased an antique for $240 and then marked up the price of [#permalink] New post   06 Jul 2022, 02:16
Could anyone please give a solution to the problem? Thanks
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Re: A dealer purchased an antique for $240 and then marked up the price of [#permalink] New post   08 Jul 2022, 21:53
nislam wrote:
Could anyone please give a solution to the problem? Thanks


Note that the value of \($240\) is irrelevant to the question since we are only dealing with percentages and not absolute numbers. We will ignore this.

For our convenience, let us assume that the dealer marked the selling price as 100. It is given that the dealer marked up the price of the antique by 40% of the selling price, which means the mark up was 40 and hence the cost price was 60.
Now, he gives a discount of 20% on the selling price, which means that the effective selling price is 80.

Hence,
Profit \(= \frac{20}{60} = 33\frac{1}{3}\%\)

So, Option B
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Re: A dealer purchased an antique for $240 and then marked up the price of [#permalink] New post   16 Jan 2024, 08:41
nislam wrote:
Could anyone please give a solution to the problem? Thanks


Let, selling price=x, marked price=0.4x, so cost price=x-0.4x=0.6x. After discount, selling price=x*0.8=0.8x.
Therefore, profit is ((0.8x-0.6x)/0.6x)*100=200/6=33.33%(B)
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Re: A dealer purchased an antique for $240 and then marked up the price of [#permalink] New post   16 Jan 2024, 11:21
nislam wrote:
A dealer purchased an antique for $240 and then marked up the price of the antique by 40 percent of the selling price. If the merchant subsequently discounted the antique by 20% of the selling price and so the antique, then what was the merchant's gross profit as a percent of his original purchase price?

(A) 25 %

(B) 33 \(\frac{1}{2 }\)%

(C) 35 %

(D) 37.5 %

(C) 40 %

\(S = 100\) (Say) , Marked Up \(= 40 =\) (Profit) {Since Mark up is the profit component only)

Thus, \(C = 60\)

Quote:
merchant subsequently discounted the antique by 20% of the selling price


So Final selling Price is \(80\)

Thus, Final profit % is \(\frac{(80-60)}{60}*100 = \frac{20}{60}*100 = 33.33\)% , Answer must be (B)
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Re: A dealer purchased an antique for $240 and then marked up the price of [#permalink]
16 Jan 2024, 11:21
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