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Bunuel
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%.

Answer B
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C/2=3R/4-C

–> C=R/2
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Bunuel
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%

\(R = 100\)

\(M_1 = 75\) ; \(P_1 = 50\)

\(C = \frac{75}{150}*100 => 50\)

Thus, to make no profit/no loss the price will have to be reduced from 100 to 50 , hence Answer must be 50% (B)
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