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

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Q. 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



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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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New post 20 Mar 2017, 04:52
Reserving this space to post the official solution. :)
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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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New post 20 Mar 2017, 07:10
EgmatQuantExpert wrote:
Q. 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
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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
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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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EgmatQuantExpert wrote:
Q. 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


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

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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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New post 20 Mar 2017, 09:29
EgmatQuantExpert wrote:
Q. 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


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

Or, Overall percentage profit or loss = \(- 9\)

Thus, answer must be (C) 9% loss...
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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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New post 20 Mar 2017, 10:10
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
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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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EgmatQuantExpert wrote:
Q. 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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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
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Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink]

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New post 09 Feb 2018, 10:49
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)
Re: Q. A seller sold two shoes at the same selling price. If the percentag   [#permalink] 09 Feb 2018, 10:49
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