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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 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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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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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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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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New post 11 Dec 2010, 15:32
That helps! Thank you so much!
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New post 11 Dec 2010, 18:48
C

Great explanation
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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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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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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
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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] 24 Oct 2015, 07:42
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