A seller sold two shoes at the same selling price. If the percentage

Question

A seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

A. 3% loss
B. 3% profit
C. 9% loss
D. 9% profit
E. No profit no Loss

Thanks,
Saquib
Quant Expert
e-GMAT

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Diwakar003 · Accepted Answer

The percentages will be 1.3x and .7y where x and y are cost prices respectively. So choosing a selling price that's LCM of 13 and 7 - let the SP be 91.

1.3x = 91. x=70.
.7y = 91. y=130.

Hence the total CP = x+y=200. SP = 91+91=182. Loss% = 200-182/200 = 9%.

Hence C

Cheers!

EgmatQuantExpert · Answer

Reserving this space to post the official solution.

rohit8865 · Answer

Let he sold each shoes for Rs 100

then for first shoe ,let original price be x
then @ 30% profit
x(1+30/100)= 100
x~ Rs 77
original price of first shoe = Rs77

similarly for second shoe 
let original price be y
y(1-30/100) =100
y~ 142
original price of first shoe = Rs142

so total of original price(CP)= 77+142 = 219
but he sold both for(SP) =Rs 100 +100= 200

Now its clear ,he is making loss
Let a be loss %
then
219(1-a/100) =200
a =~9
he is making loss of 9%

Ans C

Abhishek009 · Answer

Overall percentage profit or loss =  - (30)^2/100

Or, Overall percentage profit or loss =  - 9

Thus, answer must be (C) 9% loss...

tapabrata · Answer

Let the cost price of the two shoes be x and y
x was sold at 30% profit and y was sold at 30% loss. And the selling prices were the same (Let the selling price be s)

so 
s=x( 1+\frac{30}{100} )=y( 1-\frac{30}{100} )
13x=7y
y= \frac{13}{7} x

Let x = 70
y=130
and s=70( 1+\frac{30}{100} )= \frac{(70*130)}{100} =91

Total selling price = 2*91=182
Total cost price = x+y=200

Since the cost price is less than the selling price, the seller incurred loss.
Loss % = \frac{200-182}{200}*100  =  \frac{(18*100)}{200} =9

Answer C

KrishnakumarKA1 · Answer

let the selling price for both shoes be 100
for first the profit is 30%. therefore the CP = 100/1.3 = 76.92
for second the loss is 30%. therfore the CP = 100/0.7 = 142.85
total CP = 219.77
SP = 200

loss = 19.77
loss% = 19.77/200 . 100 = 9.88% or 9% loss

hellosanthosh2k2 · Answer

Let selling price be 91 (LCM of 13 and 7)

Shoe1 : 1.3 s1 = 91 => s1 = 70
Shoe2 : 0.7 s2 = 91 => s2 = 130

Profit or loss = 182/(130+70) = 91/100 => 9% loss (C)

ScottTargetTestPrep · Answer

We can let the selling price of each shoe = $91. Thus, for the shoe that has 30% profit, the purchasing cost, x, can be determined by the equation:

x(1.3) = 91

x = 91/1.3 = 70

Likewise, for the shoe that has 30% loss, the purchasing cost, y, can be determined by the equation:

y(0.7) = 91

x = 91/0.7 = 130

Therefore, the total cost of the two shoes is 70 + 130 = $200 and the total revenue of the two shoes is 2(91) = $182. Therefore, the percent change is (182 - 200)/200 = -18/200 = -9%, i.e., the seller has a 9% loss.

Answer: C

EMPOWERgmatRichC · Answer

Hi All,

We're told that a seller sold two shoes at the SAME selling price; the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%. We're asked for the overall percentage profit or loss made by the seller. This question can be solved by TESTing VALUES - and the answer choices are sufficiently 'spread out' that we don't have to worry about trying to find the 'perfect' numbers to TEST: the number 100 will be fine.

To start, we have to create two equations to figure out the individual profit and loss described (we can set the selling price for each shoe at $100):

The shoe that was sold for a 30% profit: 
X + .3X = $100 
1.3X = $100 
X = 100/1.3 = 1000/13 = about $77 --> this is a PROFIT of $100 - $77 = $23

The shoe that was sold for a 30% loss: 
Y - .3Y = $100 
.7Y = $100 
Y = 100/.7 = 1000/7 = about $143 --> this is a LOSS of $143 - $100 = $43

Thus, the 'net' of the two sales is $23 - $43 = - $20 --> a LOSS of about $20

Since the total sale price of the two shoes is $100 + $100 = $200, we know that $20 is 10%, so the LOSS was about a 10% loss. There's only one answer that makes sense...

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

avnish77 · Answer

When 2 items are sold at same SP, suppose x, one at a profit of p% other at a loss of p%.

There is an overall loss given by p^2/100 %.

Here we have p = 30%.

Loss = 30*30/100 %
= 9%

reynaldreni · Answer

seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller?
Original price of shoes be x & y
Selling price be p
P = 1.3x & P = 0.7y
1.3x = 0.7y
y = 13/7 x

Original total cost = x+y = 20/7x
Total selling price ,= 1.3x+0.7y = 26/10x

Overall profit/loss =(26/10 - 20/7) / (20/7) = -18/200 = -9/100 
Hence Loss of 9% (C)

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eabhgoy · Answer

Assume SP = 100 for both

CP for first at profit of 30%  
100 = (1 + (30/100))*x 
x = 100/1.3 ~ 77

CP for second at loss of 30% 
100 = (1 - (30/100))*x 
x = 100/0.7 ~ 142.85

Total SP = 200
Total CP = 77 + 142.85 = 219.85
Loss = (219.85-200)/2 = 9.875% i.e. 9% loss

Hence C

yashna36 · Answer

Hi  fskilnik ,

PLease help me with this problem. my method is bit long but I want to find the flaw in my reasoning

Let SP=X, CP=Y therefore 30 = ((x-y)/y)*100
100x-100y=30y =>130y =100x=>x=13y/10 => Total SP (x)= 2x = 2(13y/10)= 13y/5

2nd case,

Let CP = y1

((y1-x)*100)/y1 = 30 => (100 y1 - 100x)/y1 = 30 => 70y1= 100(13y/10) => 70y1 = 130y
y1= 130y/70= 13y/7 => Total CP = y + 13y/7 = 20y/7

Overall loss %, ((20y/7-13y/5)/y) comes to aprrox 25%..

where have I gone wrong?..pls help

eabhgoy · Answer

Hi yashna36 , So you were right till the last step

You just mixed up what you considered as Total CP & Total SP P/L = \frac{(CP-SP)}{CP} (In your formula the denominator of Total Cost Price was incorrect) CP = \frac{20y}{7} SP = \frac{13y}{5} P/L = ( \frac{20y}{7} - \frac{13y}{5} )/ \frac{20y}{7} = \frac{9y}{100y} = 9% loss as CP>SP

yashna36 · Answer

eabhgoy , oh yes yes!!silly silly mistake.. denominator had to be the total CP. Thankyou so much

fskilnik · Answer

It seems (from the posts above) your doubts are gone. Thank you for helping  yashna36 ,  eabhgoy !

Regards,
Fabio.

exc4libur · Answer

price(quantity) - cost = net 
 (pq-c)/c=net{%}

(x-a)/a=0.3…x-a=0.3a…x=1.3a…a=x/1.3…(cost.a) 
 (x-b)/b=-0.3…x=-0.3b+b…b=x/0.7…(cost.b)

\frac{x(2)-(cost.a+cost.b)}{cost.a+cost.b}=\frac{2x-(x/1.3+x/0.7)}{x/1.3+x/0.7}=\frac{182x-200x/91}{200x/91}=\frac{-18x/91}{200x/91}=…

(-18x/91)(91/200x)=-18/200=-9/100=-0.09

Answer (C)

Kinshook · Answer

Given; A seller sold two shoes at the same selling price.

Asked; If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

Let the selling price be x

the percentage profit on one of the shoes was 30%

Cost price of the shoe = x/1.3

the percentage loss on the other shoe was 30%

Cost price of the shoe = x/.7

overall profit or loss made by the seller = 2x - x/1.3 - x/.7 = - 19.78%x

overall percentage profit or loss made by the seller = -19.78%x / (x/1.3+x/.7) = -9%

IMO C

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A seller sold two shoes at the same selling price. If the percentage

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