Bobby bought two shares of stock, which he sold for $96 each. If he

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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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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Let x = the ORIGINAL purchase price of the stock that had a PROFIT of 20%
So, 1.2x = the SALE price when Bobby sold the stock for a profit of 20%
Since Bobby sold that stock for $96, we can write: 1.2x = 96
Solve to get: x = $80

Let y = the ORIGINAL purchase price of the stock that had a LOSS of 20%
So, 0.8x = the SALE price when Bobby sold the stock for a loss of 20%
Since Bobby sold that stock for $96, we can write: 0.8x = 96
Solve to get: y = $120

This means the total cost of Bobby's ORIGINAL purchase = $80 + $120 = $200
The total SALE price of the two stocks = $96 + $96 = $192

So, Bobby lost a total of $8 in this transaction.

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?

That helps! Thank you so much!

C

Great explanation

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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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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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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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

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

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

(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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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
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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 %)

CP of first stock is \(\frac{96}{1.2} =80\)
CP of second stock is \(\frac{96}{0.8} =120\)

CP of 2 stock is 200 ; SP of 2 stocks is 96*2 = 192

Thus, There is a loss of $8 , Answer will be (C)
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