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Bobby bought 2 shares, and which he sold for $96 each. If he

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Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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New post 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
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Re: Profit problem  [#permalink]

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New post 11 Dec 2010, 14:57
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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

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

Answer: C.
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Re: Profit problem  [#permalink]

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New post 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]

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New post 11 Dec 2010, 15:17
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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]

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New post 11 Dec 2010, 15:32
That helps! Thank you so much!
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Re: Profit problem  [#permalink]

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New post 11 Dec 2010, 18:48
C

Great explanation
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Re: Profit problem  [#permalink]

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New post 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.
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Re: Profit problem  [#permalink]

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New post 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.
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Re: Profit problem  [#permalink]

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New post 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
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Re: Profit problem  [#permalink]

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New post 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.
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Re: Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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Re: Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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New post 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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Re: Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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New post 22 Jul 2014, 22:38
2
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
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Re: Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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New post 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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Re: Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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New post 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]

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New post 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

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Re: Bobby bought 2 shares, and which he sold for $96 each. If he  [#permalink]

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New post 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 %)
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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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