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

Question

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%

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

Akash720 · Answer

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

pushpitkc · Answer

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.

generis · Answer

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

SchruteDwight · Answer

C/2=3R/4-C

–> C=R/2

Abhishek009 · Answer

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)

bumpbot · Answer

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

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

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