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Word Problem - Profit and loss

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by singhmaharaj » Tue May 06, 2014 5:11 am
Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had

A) a profit of $ 10

B) a profit of $ 8

C) a loss of $ 8

D) a loss of $ 10

E) nether a profit nor a loss
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by GMATGuruNY » Tue May 06, 2014 5:14 am
Bobby bought two shares of stock, which sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined bobby had:

a: a profit of $10
b: a profit of $8
c: a loss of $8
d: a loss of $10
e: neither profit nor loss
Many students struggle with this type of question.
An efficient way to solve that involves very little algebra is to GUESS AND CHECK.

Since all of the values in the problem and in the answer choices are integers, the purchase prices are almost certainly each a multiple of a 10.

Stock sold at a 20% profit:
Since this stock is sold at a PROFIT, the purchase price = a multiple of 10 LESS than 96.
90 + .2(90) = 108. Too big.
80 + .2(80) = 96.
Success!
The purchase price = 80.
Profit = 96-80 = 16.

Stock sold at a 20% loss:
Since this stock is sold at a LOSS, the purchase price = a multiple of 10 GREATER than 96.
100 - .2(100) = 80. Too small.
110 - .2(110) = 88. Too small.
120 - .2(120) = 96.
Success!
The purchase price = 120.
Loss = 96-120 = -24.

Profit + loss = 16 + (-24) = -8.
A loss of $8.

The correct answer is C.
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by GMATGuruNY » Tue May 06, 2014 5:23 am
Bobby bought two shares of stock, which sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined bobby had:

a: a profit of $10
b: a profit of $8
c: a loss of $8
d: a loss of $10
e: neither profit nor loss
Algebraic solution:

$96 yields a 20% PROFIT:
Thus, this stock is sold for 120% of its cost:
96 = (120/100)x
96 = (6/5)x
x = (96*5)/6
x = 16*5
x = 80.

$96 yields a 20% LOSS:
Thus, this stock is sold for 80% of its cost:
96 = (80/100)y
96 = (4/5)y
y = (96*5)/4
y = 24*5
y = 120.

Total cost = x+y = 80+120 = 200.
Total revenue = 96+96 = 192.
Revenue - cost = 192-200 = -8.
A loss of $8.

The correct answer is C.
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by Jeff@TargetTestPrep » Mon Dec 11, 2017 11:29 am
singhmaharaj wrote:Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had

A) a profit of $ 10

B) a profit of $ 8

C) a loss of $ 8

D) a loss of $ 10

E) nether a profit nor a loss
We are given that Bobby bought 2 shares, which he sold for $96 each, and that he made a 20% profit on the sale of one share and had a loss of 20% on the sale of the other share. We can set up the following equations in which c = the cost of the first share and d = the cost of the second share.

For the first share, with a profit of 20% we have:

Profit = 0.2c

Since profit = revenue - cost, we have:

96 - c = 0.2c

96 = 1.2c

c = 80

Thus, the profit for the first share was 96 - 80 = 16 dollars.

For the 20% loss we have:

Profit = -0.2d

Since profit = revenue - cost, we have:

96 - d = -0.2d

96 = 0.8d

d = 120

Thus, the loss for the second share was 96 - 120 = 24 dollars.

Since Bobby has a profit of 16 dollars and a loss of 24 dollars, he has a net loss of 8 dollars.

Answer: C

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