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11 Dec 2010, 15:44
5
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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 ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 56244 Re: Profit problem [#permalink] ### Show Tags 11 Dec 2010, 15:57 5 3 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

Cost of the first stock: 96/1.2=80, so profit from it 96-80=16
Cost of the second stock: 96/0.8=120, so loss from it 96-120=-24

Overall loss 16-24=-8

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11 Dec 2010, 16:03
I may not be understanding the formula for the 'Cost of the stock' do you mind elaborating on this?

i.e. 96/1.2?
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11 Dec 2010, 16:17
2
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?

He had a profit of 20% on the sale of the first stock, so if he bought it for $x then x+0.2x=1.2x=96 --> x=96/1.2=80 --> profit 96-x=96-80=16; He had a loss of 20% on the sale of the second stock, so if he bought it for$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.
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11 Dec 2010, 16:32
That helps! Thank you so much!
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11 Dec 2010, 19:48
C

Great explanation
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12 Dec 2010, 05:42
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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. _________________ 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 > Manager Joined: 16 Feb 2011 Posts: 190 Re: Profit problem [#permalink] ### Show Tags 10 Sep 2011, 07:29 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.
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11 Sep 2011, 01:27
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
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11 Sep 2011, 10:12
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 Answer is C. Math Expert Joined: 02 Sep 2009 Posts: 56244 Re: Bobby bought 2 shares, and which he sold for$96 each. If he  [#permalink]

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10 Jun 2013, 05:09
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22 Jul 2014, 23:38
3
First Share sold at 96 which includes 20% profit

Cost Price $$= \frac{96*100}{120} = 80$$

Second Share sold at 96 which includes 20% loss

Cost Price$$= \frac{96 * 100}{80} = 120$$

Total Cost Price = 120 + 80 = 200

Total Selling Price = 96 * 2 = 192

Loss = 8

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15 Sep 2018, 17:41
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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14563 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Bobby bought 2 shares, and which he sold for$96 each. If he  [#permalink]

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23 Sep 2018, 11:49
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

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05 Oct 2018, 03:15
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 %)
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Re: Bobby bought two shares of stock, which he sold for $96 [#permalink] ### Show Tags 30 Apr 2019, 06:31 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Bobby bought two shares of stock, which he sold for$96   [#permalink] 30 Apr 2019, 06:31
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