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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 percentag  [#permalink]

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Updated on: 07 Aug 2018, 06:19
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65% (hard)

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64% (02:04) correct 36% (01:50) wrong based on 95 sessions

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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

Thanks,
Saquib
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Originally posted by EgmatQuantExpert on 20 Mar 2017, 05:50.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:19, edited 1 time in total.
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Re: Q. A seller sold two shoes at the same selling price. If the percentag  [#permalink]

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20 Mar 2017, 05:52
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Re: Q. A seller sold two shoes at the same selling price. If the percentag  [#permalink]

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20 Mar 2017, 08:10
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
Quant Expert
e-GMAT

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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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20 Mar 2017, 09:57
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1
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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20 Mar 2017, 10:29
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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20 Mar 2017, 11:10
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

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

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21 Mar 2017, 03:46
1
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

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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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09 Feb 2018, 11:49
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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 &nbs [#permalink] 09 Feb 2018, 11:49
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