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

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Difficulty:   85% (hard)

Question Stats: 56% (02:17) correct 44% (01:54) wrong based on 237 sessions

### HideShow timer Statistics 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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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.
e-GMAT Representative V
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Re: Q. A seller sold two shoes at the same selling price. If the percentag  [#permalink]

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Reserving this space to post the official solution. _________________
Director  D
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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

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 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

Cheers!
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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

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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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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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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1
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)
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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

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 _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14590 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Q. A seller sold two shoes at the same selling price. If the percentag [#permalink] ### Show Tags 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...

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Intern  Joined: 20 Feb 2018
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Re: Q. A seller sold two shoes at the same selling price. If the percentag  [#permalink]

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

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

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

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

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

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1
eabhgoy,

oh yes yes!!silly silly mistake.. denominator had to be the total CP. Thankyou so much GMATH Teacher P
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Re: Q. A seller sold two shoes at the same selling price. If the percentag  [#permalink]

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1
yashna36 wrote:
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

---

where have I gone wrong?..pls help

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

Regards,
Fabio.
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Our high-level "quant" preparation starts here: https://gmath.net Re: Q. A seller sold two shoes at the same selling price. If the percentag   [#permalink] 15 Nov 2018, 10:22
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