The percentage profit earned by selling an article for $1920 is equal

Question

The percentage profit earned by selling an article for $1920 is equal in the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit?

A) 2000
B) 2200
C) 2400
D) 2600
E) 2800

A) 2000
B) 2200
C) 2400
D) 2600
E) 2800

mj12345 · Answer

Percent Profit/Loss = x

C + xC = 1920
C - xC = 1280

Solving for C => 2C = 3200 => C = 1600

Sale Price with 25% profit => 1.25*1600 = 2000. So, answer is A.

philipssonicare · Answer

I've got no idea what the above explanation is (not saying it's wrong). Someone please explain it.

Percent profit = |Percent loss|, since percent loss will be a negative, can represent it as -(percent loss)

(1920-x)/x = -(1280-x)/x
Multiply both sides by x
(1920-x)=x-1280
3200=2x
1600=x

This solves for x, but not for the 25% increase from x

125/100·1600=5·400=2000

A

ksrutisagar · Answer

Let the percentage (profit or Loss) in each case be x%

Let the cost price be $C

Then , 1920 = C *  \frac{(100 + x )}{100}  (Profit of x%)
 1280 = C *  \frac{(100 - x)}{100}  (Loss of x%)

Adding the two equations,

1920 + 1280 = 2C

C = 1600

Now, to make 25% profit,

Selling Price = 1600 * \frac{125}{100}

= 2000 Choice A

gota900 · Answer

Bunuel , could you please step in here? No explanation seems to do the trick sufficiently...

I'm confused!

Bunuel · Answer

Here is an easy solution: https://gmatclub.com/forum/the-percenta ... l#p1941691 C there stands for the COST. Recall that both profit and loss are calculated on the cost of an item.

Archit3110 · Answer

(1920-x)/x = (x-1280)/x

x= 1600

x-1600/1600 = 25/100

x = $2000 IMO A

Abhishek009 · Answer

CP is  \frac{1920 + 1280}{2} = 1600

SP of the item at 25% profit is  1600*\frac{5}{4} = 2000 , Answer must be (A)

nivivacious · Answer

Since we're told Loss % = Profit %; the CP should be somewhere in between Loss and Profit.
Hence 1920+1280/2 = CP
Therefore 1600 = CP
We need to find 25% profit
1600 x 125/100 is approximately 2000
Hence A

The percentage profit earned by selling an article for $1920 is equal

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The percentage profit earned by selling an article for $1920 is equal

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