M03-32

Official Solution:

A car dealership sold two cars: Car A at a 10% profit and Car B at a 10% loss, resulting into an overall profit of 5% from the two sales. If the dealership's profit from these two cars was $1,000, what was the initial cost of cars A and B?

A. $5,000 and $1,000
B. $9,000 and $5,000
C. $11,000 and $9,000
D. $15,000 and $5,000
E. $20,000 and $10,000


Since the dealership had an overall profit of 5% and that equals to $1,000, we can determine that the total cost price of the two cars was $20,000 (0.05*x = 1,000 giving x = 20,000).

Among the options, only options C and D give the total cost price of the two cars as $20,000. Let's check one of them:

C. Cost prices of the two cars are given as $11,000 and $9,000. The profit from the first car would be \(0.1*$11,000=$1,100\) and the loss from the second car would be \(0.1*$9,000=$900\). So, the overall profit would be \($1,100-$900=$200\), which is not equal to the total profit of $1,000. Therefore, option C is incorrect.

So, we are left with only option D, which must be correct.


Answer: D