When a person sells two items $1656 each, one at a gain of 20% and the

Question

When a person sells two items $1656 each, one at a gain of 20% and the other at a loss of 20%, then the seller incurs a loss or gain of:

A. no loss no gain
B. 20 % profit
C. 4% loss
D. 2% profit
E. 2% loss.

tiruraju · Accepted Answer

I understood the question the following way

The 2 items are sold at 1656 each , one at a profit of 20% and the other at a loss of 20%

So the original rates of the items are 1380 and 2070 respectively
So the total he spend for those 2 items is 3450 but he ended up in selling them with (1656*2) 3312

So the loss is 3450 - 3312 = 138
The loss percentage is (138/3450) *100 = 4% loss - Answer C

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KarishmaB · Answer

Tiruraju, Adishail and Ian have already explained the solution quite well so I will not repeat it, though I do want to add the following notes.

Note I: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.

Note II: When two items are bought at the same price and then one is sold at a profit of a% and the other is sold at a loss of a% (which means one is sold at selling price which is higher than cost price and the other is sold at selling price which is lower than cost price), there is no profit, no loss.

Confirm using examples. Get back to me if you need the derivation of the formula above.

prab · Answer

say the price of the bike is 100, 
so he bought it in 120, since he paid 20% extra. Now again he sold the bike in 124, so he has $ 4 as profit.

(4/120)*100 = 3.33% profit.

eladshus · Answer

Hope that I understood the question correctly, but if he sells 2 items separately and their original price was the same - there should be no profit or loss..

pick numbers:
Product 1 = 100, 20 % gain = 20, Sell price = 120
Product 2 = 100, 20% loss = 20, Sell price = 80

If you sum both up, you should get 120+80 = 200 which is the same as if he would have sold both of them in the original price (100 + 100 = 200)

metallicafan · Answer

I agree with eladshus. IMO is A.
However, I think that the question has a problem; it doesn't mention whether the products cost the same amount.

prab · Answer

I missunderstood the question completely. + 1 for A

prab · Answer

well the question i was solving for is some what like.... if a buys a bike with a loss of 20 % and again sells the bike with a profit of 20%, what was his profit or loss......

so for this the solution below fits rite ?

say the price of the bike is 100, 
so he bought it in 120, since he paid 20% extra. Now again he sold the bike in 124, so he has $ 4 as profit.

(4/120)*100 = 3.33% profit.

adishail · Answer

C

Two items, A and B

1.2A = 1656 => A = 1656/1.2 = 1380
0.8B = 1656 => B = 1656/0.8 = 2070

Profit from A = 1656 - 1380 = 276
Profit from B = 1656 - 2070 = -414 (loss)

Total loss or profit = 276-414 = -138

Loss % for A & B = -138 / (1380+2070) = - 4% ======== 4 % Loss !

IanStewart · Answer

The selling price here is the *final* price, not the *starting* price. The answer is not A; that's the trap.

We know we sold two items for $x each (it doesn't actually matter what x is, only that it's the same for both items, and the number in the question seems awkward to work with, so I'll use a letter instead). If we bought the first item for $b, we know we made 20%:

$b ----(+20%)---> $x

so x = 1.2b, or b = 5x/6.

If the other item cost $c, we know we lost 20%:

$c ----(-20%)----> $x

so x = 0.8c, or c = 5x/4.

So we bought the two items for $(b+c) = $(5x/6 + 5x/4) = $25x/12, and sold them for $2x. Thus, overall, we took a loss of $(x/12) on our initial purchase price of $(25x/12). So the percent loss is 100% * (x/12)/(25x/12) = 100% * (1/25) = 4%.

Wofford · Answer

I am still confused

adishail · Answer

The selling price for both items is $1656. One was sold at 20% profit and one at 20% loss. Therefore,

The cost (A) of one item was below $1656 -------- A + A*20/100 = $1656 (sold at a profit)

The cost (B) of second item was above $1656 -------- B - B*20/100 = $1656 (sold at a loss)

Wofford · Answer

Ahhh got it now. Thanks Karishma.

anandthiru · Answer

excellent question....

gmat1011 · Answer

Super tip - thx Karishma

Knowing the (a^2/100)% formula when same SP AND same % of loss and gain is a real time saver. Thanks.

KarishmaB · Answer

Glad it helped gmat1011, though formulae come with a caveat. 
Formulae will take you only some of the way, the rest you need to get through using logic and conceptual understanding of the topic. There will be times (such as higher level questions) when formulae may not be applicable. That said, once you understand the topic and concepts involved, using a formula, when relevant, can be a real time saver.

letlovebethejudge · Answer

GMAT expects us to solve the questions within 2 mins. 
For that, remember this formula
When the SP is same and Gain and Profit % is common, the Loss % = (Common gain/loss%)^2/100
And the formula for loss amount is = 2 X (Common gain/loss%)^2 X Selling Price/(100^2-(Common gain/loss%)^2)

So answer is 20^2/100 = 400/100=4
C

Namansondhi · Answer

Whenever we have a percentage increase and a decrease by the same number and the question asks us to calculate the overall profit or loss, there is an overall loss by the value of x^2/100 , where x is the percentage increase and decrease as given in the question.

Here the overall loss will be given as 20^20/100 = 400/100 = 4% loss

Here the overall loss will be given as 20^20/100 = 400/100 = 4% loss

Pipi0914 · Answer

it takes a lot of time to compute the actual number. Suggest that we keep 1656 in the equation because it will be canceled out eventually.

blonpina · Answer

Given that they proceeds have same $ amount we can geometrically link the returns:

Gain = (1+20%)*(1-20%)-1 = (1.2*0.8)-1=0.96-1=-0.04=-4%

When a person sells two items $1656 each, one at a gain of 20% and the

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