Question 1081202
Let
x = original value of book1
y = original value of book2
this is at the point in time when you are buying each book (not selling)


you bought book1 for x dollars and turn around to sell it for 990 dollars. The difference in price is 990-x which is some positive number (since you gain money for selling this book). 


Divide this difference over the original price x to get (990-x)/x. This ratio will result in the decimal value 0.10 which represents a 10% gain. So we have this equation (990-x)/x = 0.10


Let's solve for x
(990-x)/x = 0.10
x*(990-x)/x = x*0.10
990-x = 0.10x
990-x+x = 0.10x+x
990 = 1.10x
1.10x = 990
1.10x/(1.10) = 990/(1.10)
x = 900


So the original value of book1 is $900. This is the value in which you buy it at.


In other words, you bought book1 for $900 and sold it $990.


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Similarly, the second equation would be 
(990-y)/y = -0.10
Notice how the right hand side is negative to indicate a loss. The left side is identical to the first equation (use y instead of x).


Solve for y
(990-y)/y = -0.10
y*(990-y)/y = y*(-0.10)
990-y = -0.10y
990-y+y = -0.10y+y
990 = 0.90y
0.90y = 990
0.90y/(0.90) = 990/(0.90)
y = 1100


So you bought book2 for $1100 and then later sold it for $990. 


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Recapping so far:
<ul><li>you buy book1 for $900 and sell it later for $990.</li></ul>
<ul><li>you buy book2 for $1100 and sell it later for $990.</li></ul>


In the case of book1, you have a profit of 
(new value) - (old value) = 990-900 = 90 dollars


In the case of book2, you have a profit of 
(new value) - (old value) = 990-1100 = -110 dollars
Note: the negative profit means a loss


The two profits (90 and -110) are then combined to get this overall net profit: 90 + (-110) = -20

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At the end of the day, the net profit comes out to -20 dollars indicating that you lost $20. 


Answer: <font color=red>Choice (a) I lost $20</font>