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Intern
Joined: 19 Oct 2010
Posts: 6
Bobby bought 2 shares, and which he sold for $96 each. If he [#permalink] ### Show Tags 11 Dec 2010, 14:44 5 11 00:00 Difficulty: 45% (medium) Question Stats: 70% (01:33) correct 30% (01:34) wrong based on 567 sessions ### HideShow timer Statistics Bobby bought 2 shares, and which he sold for$96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

A) a profit of 10
B) a profit of 8
C) a loss of 8
D) a loss of 10
E) neither a profit nor a loss
Math Expert
Joined: 02 Sep 2009
Posts: 50544
Re: Profit problem  [#permalink]

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11 Dec 2010, 14:57
5
2

He had a loss of 20% on the sale of the second stock, so if he bought it for $y then y-0.2y=0.8y=96 --> y=96/0.8=120 --> loss y-96=120-96=24; Overall loss: 24-16=8. Hope it's clear. _________________ Intern Joined: 19 Oct 2010 Posts: 6 Re: Profit problem [#permalink] ### Show Tags 11 Dec 2010, 15:32 That helps! Thank you so much! Senior Manager Status: Bring the Rain Joined: 17 Aug 2010 Posts: 352 Location: United States (MD) Concentration: Strategy, Marketing Schools: Michigan (Ross) - Class of 2014 GMAT 1: 730 Q49 V39 GPA: 3.13 WE: Corporate Finance (Aerospace and Defense) Re: Profit problem [#permalink] ### Show Tags 11 Dec 2010, 18:48 C Great explanation _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8521 Location: Pune, India Re: Profit problem [#permalink] ### Show Tags 12 Dec 2010, 04:42 2 2 Yellow22 wrote: Bobby bought 2 shares, and which he sold for$96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

A) a profit of 10
B) a profit of 8
C) a loss of 8
D) a loss of 10
E) neither a profit nor a loss

I am no fan of formulas, especially the unintuitive ones still, this little formula has proved useful because of the tedious calculations involved otherwise.

When two items are sold at the same price, one at a profit of a% and other at a loss of a%, there will always be a loss of $$\frac{(a^2)}{100} %$$. e.g. Here a = 20, so loss % = $$\frac{(20)^2}{100} %$$ = 4%.
Total Sale Price = Cost Price - Loss% of Cost Price
192*(100/96) = Cost Price
Cost Price = $200 Loss =$200 - $192 =$8

Get back to me if you need the derivation of the formula above.
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Joined: 15 Feb 2011
Posts: 205
Re: Profit problem  [#permalink]

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10 Sep 2011, 06:29
VeritasPrepKarishma wrote:
Yellow22 wrote:
Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had... A) a profit of 10 B) a profit of 8 C) a loss of 8 D) a loss of 10 E) neither a profit nor a loss I am no fan of formulas, especially the unintuitive ones still, this little formula has proved useful because of the tedious calculations involved otherwise. When two items are sold at the same price, one at a profit of a% and other at a loss of a%, there will always be a loss of $$\frac{(a^2)}{100} %$$. e.g. Here a = 20, so loss % = $$\frac{(20)^2}{100} %$$ = 4%. Total Sale Price = Cost Price - Loss% of Cost Price 192*(100/96) = Cost Price Cost Price =$200
Loss = $200 -$192 = $8 Get back to me if you need the derivation of the formula above. Hi Karishma, Thanks for letting us know the formula...i wasnt aware of it...nonetheless, can you pls help me understand the usage of the formula in this particular question.. Thanks. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8521 Location: Pune, India Re: Profit problem [#permalink] ### Show Tags 11 Sep 2011, 00:27 DeeptiM wrote: VeritasPrepKarishma wrote: Yellow22 wrote: Bobby bought 2 shares, and which he sold for$96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

A) a profit of 10
B) a profit of 8
C) a loss of 8
D) a loss of 10
E) neither a profit nor a loss

I am no fan of formulas, especially the unintuitive ones still, this little formula has proved useful because of the tedious calculations involved otherwise.

When two items are sold at the same price, one at a profit of a% and other at a loss of a%, there will always be a loss of $$\frac{(a^2)}{100} %$$. e.g. Here a = 20, so loss % = $$\frac{(20)^2}{100} %$$ = 4%.
Total Sale Price = Cost Price - Loss% of Cost Price
192*(100/96) = Cost Price
Cost Price = $200 Loss =$200 - $192 =$8

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

Hi Karishma,

Thanks for letting us know the formula...i wasnt aware of it...nonetheless, can you pls help me understand the usage of the formula in this particular question..

Thanks.

The formula is that when two items are sold at the same selling price, one at a profit of a% and the other at a loss of a%, there is an overall loss. The loss% = $$\frac{(a^2)}{100} %$$.

Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had... Here the two shares are sold at the same selling price. One at a profit of 20% and the other at a loss of 20%. So loss % = $$\frac{(20)^2}{100} %$$ = 4%. But we need the amount of loss. Total Sale price of the two shares = 2*96 = 192 Since there is a loss of 4%, the 96% of the total cost price must be the total sale price (96/100)*Cost Price = 192 Cost Price =$200
Loss = $200 -$192 = $8 _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > GMAT self-study has never been more personalized or more fun. Try ORION Free! Director Joined: 01 Feb 2011 Posts: 664 Re: Profit problem [#permalink] ### Show Tags 11 Sep 2011, 09:12 lets say cost of each shares are x and y respectively. Selling price = 120x/100 and 80y/100 respectively = 96 120x/100 = 96 => x=80 80y/100 = 96 => y =120 => together cost = x+y = 200 together selling price = 2*96 = 192 => loss of$8

Math Expert
Joined: 02 Sep 2009
Posts: 50544

### Show Tags

25 Jun 2013, 23:21
Total SP = 2*96
Total CP = CP1

The formula for calculating loss % when SP is same = (x/10) ^2
So here x = 20
%loss = (20/10)^2 = 2^2 = 4% loss

We know SP = 92*2 ( 2 items)
loss % = 4
Now calc CP => SP = CP(1-loss/100) = CP (1-4/100) = CP*96/100

2*96 = CP * 96/100 => CP = 200
Total loss is 4% of CP => 4*200/100 = 8
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### Show Tags

07 Sep 2014, 08:15
Yellow22 wrote:
I may not be understanding the formula for the 'Cost of the stock' do you mind elaborating on this?

i.e. 96/1.2?

SP= 100% of CP + profit
SP= 100% of CP + 20% of CP
SP= 120% of CP

therefore CP= SP/120%
= 96*100/120
= 80

Similarly,

SP= 100% of CP - Loss
= 100% of CP - 20% of CP
= 80% of CP

CP = SP*100/80
=96*100/80
=120
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Status: GMATH founder
Joined: 12 Oct 2010
Posts: 464
Re: Bobby bought 2 shares, and which he sold for $96 each. If he [#permalink] ### Show Tags 15 Sep 2018, 16:41 Yellow22 wrote: Bobby bought 2 shares, and which he sold for$96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...

A) a profit of 10
B) a profit of 8
C) a loss of 8
D) a loss of 10
E) neither a profit nor a loss

(Common) Assumption: although not explicitly mentioned, we are dealing with profit of 20% over the cost on the corresponding sale. The same for the loss.

$$?\,\,\,:\,\,\,{\text{profit/loss}}\,\,\left( \ \right)$$

$$1{\text{st}}\,\,{\text{share}}:\,\,\,\,\,96 = \,\,\left( {1 + \frac{1}{5}} \right)\,\,{\text{cost}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{cost}} = \frac{5}{6}\left( {96} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{profit}} = \frac{1}{6}\left( {96} \right) = \underleftrightarrow {\frac96{6}} = 16\,\,\,\left( \ \right)$$

$$2{\text{nd}}\,\,{\text{share}}:\,\,\,\,\,96 = \,\,\left( {1 - \frac{1}{5}} \right)\,\,{\text{cost}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{cost}} = \frac{5}{4}\left( {96} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{loss}} = \frac{1}{4}\left( {96} \right) = \underleftrightarrow {\frac96{4}} = 24\,\,\left( \ \right)$$

$$?\,\, = \,\,\,16 + \left( { - 24} \right) = - 8\,\,\left( \ \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Bobby bought 2 shares, and which he sold for $96 each. If he [#permalink] ### Show Tags 23 Sep 2018, 10:49 Hi All, We're told that Bobby bought 2 shares, which he sold for$96 each, he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share. We're asked to find the TOTAL profit or loss on the sale of the two shares. This question essentially comes down to creating two equations and then solving for the original purchase price of each share.

The 20% profit share --> X + .2X = 96
The 20% loss share --> Y - .2Y = 96

1.2X = 96
12X = 960
X = 960/12 = $80 For the first share, the PROFIT was$96 - $80 =$16

.8Y = 96
8Y = 960
Y = 960/8 = $120 For the second share, the LOSS was$120 - $96 =$24

$16 profit -$24 loss = Total LOSS of $8 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Posts: 12
Re: Bobby bought 2 shares, and which he sold for $96 each. If he [#permalink] ### Show Tags 05 Oct 2018, 02:15 Gain = (S.P.) - (C.P.) Loss = (C.P.) - (S.P.) Loss or gain is always reckoned on C.P. Gain Percentage: (Gain %) Gain % = Gain x 100 C.P. Loss Percentage: (Loss %) Loss % = Loss x 100 C.P. Selling Price: (S.P.) SP = (100 + Gain %) x C.P 100 Selling Price: (S.P.) SP = (100 - Loss %) x C.P. 100 Cost Price: (C.P.) C.P. = 100 x S.P. (100 + Gain %) Cost Price: (C.P.) C.P. = 100 x S.P. (100 - Loss %) Re: Bobby bought 2 shares, and which he sold for$96 each. If he &nbs [#permalink] 05 Oct 2018, 02:15
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# Bobby bought 2 shares, and which he sold for \$96 each. If he

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