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# When a retailer marks down a scarf by 25%, it still makes a 50% profit

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Math Expert
Joined: 02 Sep 2009
Posts: 47918
When a retailer marks down a scarf by 25%, it still makes a 50% profit  [#permalink]

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31 Jul 2018, 21:40
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Difficulty:

35% (medium)

Question Stats:

67% (01:15) correct 33% (01:50) wrong based on 39 sessions

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When a retailer marks down a scarf by 25%, it still makes a 50% profit over the price at which it originally purchased the scarf. By what percent would the retailer have to mark down the scarf to make no profit nor loss from the sale?

A. 25%
B. 50%
C. 60%
D. 75%
E. 95%

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Re: When a retailer marks down a scarf by 25%, it still makes a 50% profit  [#permalink]

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31 Jul 2018, 22:06
1
Bunuel wrote:
When a retailer marks down a scarf by 25%, it still makes a 50% profit over the price at which it originally purchased the scarf. By what percent would the retailer have to mark down the scarf to make no profit nor loss from the sale?

A. 25%
B. 50%
C. 60%
D. 75%
E. 95%

Assume the present price of scarf to be 100
Mark down price = 25% of 100 = 100 -25 = 75
75 rs is still a profit of 50%, therefore Original price = 50

The price which the retailer needs to mark down for no profit no loss is 100 -50 = 50, which is 50%

Hence B
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When a retailer marks down a scarf by 25%, it still makes a 50% profit  [#permalink]

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31 Jul 2018, 23:26
Bunuel wrote:
When a retailer marks down a scarf by 25%, it still makes a 50% profit over the price at which it originally purchased the scarf. By what percent would the retailer have to mark down the scarf to make no profit nor loss from the sale?

A. 25%
B. 50%
C. 60%
D. 75%
E. 95%

If the scarf is marked down by 25%,
a scarf costing $$200$$ would be available for $$\frac{3}{4}*200 = 150$$

Since we are still making a 50% profit, the cost price of the scarf is $$\frac{150}{1.5} = 100$$

Therefore, the scarf would be sold for $100 less which is $$\frac{100}{200}$$ or 50%(Option B) at it's original price. _________________ You've got what it takes, but it will take everything you've got SC Moderator Joined: 22 May 2016 Posts: 1903 When a retailer marks down a scarf by 25%, it still makes a 50% profit [#permalink] ### Show Tags 01 Aug 2018, 16:58 Bunuel wrote: When a retailer marks down a scarf by 25%, it still makes a 50% profit over the price at which it originally purchased the scarf. By what percent would the retailer have to mark down the scarf to make no profit nor loss from the sale? A. 25% B. 50% C. 60% D. 75% E. 95% When a retailer marks down a scarf by 25%, it still makes a 50% profit over the original cost Let the original price be$100. The retailer marks that price down by 25%. The new price is $75 Let C = original cost Let S = sell price Profit = $$(S-C)=(75 - C)$$ AND Profit from sale at$75 = $$.50C$$

Equate both definitions of profit
$$75 - C = .50C$$
$$75=1.5C$$
$$C=\frac{75}{1.5}=\frac{750}{15}=50$$

Now we want profit/loss to equal 0. At what sell price does profit/loss = $0? New sell price, $$S_2$$, is? $$(S_2-C)=0$$ $$S_2-50=0$$ $$S_2=50$$ $$50$$ is the sell price at which profit/loss =$0

Original $$S = 100$$
New $$S_2 = 50$$

$50 is what percent less than$100?
Percent change: $$\frac{New-Old}{Old}*100$$

Percent change: $$(\frac{50-100}{100}*100=(\frac{-50}{100}*100)$$

$$=(-0.50*100)=-50$$ percent

The retailer must mark down the original \$100 sell price by 50%.

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When a retailer marks down a scarf by 25%, it still makes a 50% profit &nbs [#permalink] 01 Aug 2018, 16:58
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