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# Bobby bought 2 shares, and which he sold for $96 each. If he  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Intern Joined: 19 Oct 2010 Posts: 7 Followers: 0 Kudos [?]: 2 [1] , given: 0 Bobby bought 2 shares, and which he sold for$96 each. If he [#permalink]  11 Dec 2010, 14:44
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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 [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 18718 Followers: 3239 Kudos [?]: 22316 [2] , given: 2613 Re: Profit problem [#permalink] 11 Dec 2010, 14:57 2 This post received KUDOS Expert's post 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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Re: Profit problem [#permalink]  11 Dec 2010, 15:03
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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Re: Profit problem [#permalink]  11 Dec 2010, 15:17
Expert's post
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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Re: Profit problem [#permalink]  11 Dec 2010, 15:32
That helps! Thank you so much!
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Re: Profit problem [#permalink]  11 Dec 2010, 18:48
C

Great explanation
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Re: Profit problem [#permalink]  12 Dec 2010, 04:42
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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 My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Profit problem [#permalink]  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: 4573 Location: Pune, India Followers: 1029 Kudos [?]: 4467 [0], given: 162 Re: Profit problem [#permalink] 11 Sep 2011, 00:27 Expert's post 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 My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Profit problem [#permalink]  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 Answer is C. Math Expert Joined: 02 Sep 2009 Posts: 18718 Followers: 3239 Kudos [?]: 22316 [0], given: 2613 Re: Bobby bought 2 shares, and which he sold for$96 each. If he [#permalink]  10 Jun 2013, 04:09
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Re: Bobby bought 2 shares, and which he sold for $96 each. If he [#permalink] 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 _________________ Thanks & Regards Yodee ‘A good plan violently executed now is better than a perfect plan executed next week.’ - General Georg S. Patton SVP Joined: 09 Sep 2013 Posts: 1723 Followers: 165 Kudos [?]: 33 [0], given: 0 Re: Bobby bought 2 shares, and which he sold for$96 each. If he [#permalink]  22 Jul 2014, 19:01
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Re: Bobby bought 2 shares, and which he sold for $96 each. If he [#permalink] 22 Jul 2014, 22:38 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 Answer = C _________________ Kindly press "Kudos" to appreciate Re: Bobby bought 2 shares, and which he sold for$96 each. If he   [#permalink] 22 Jul 2014, 22:38
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