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Car Dealer

by golu23 » Fri Jan 06, 2012 5:27 am
A used car dealer sold one car for a profit of 25% of the purchase price and another car for a 20% loss I f the dealer sold each car for $20000,what was the dealer's total profit or loss, in dollars for the two trans actions?
Options 1000 profit,
2000 profit,
1000 loss,
2000 loss,
3334 loss
really confused with this one and it keeps appearing frequently on GMAT PREP plz help.
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by Anurag@Gurome » Fri Jan 06, 2012 5:37 am
golu23 wrote:A used car dealer sold one car for a profit of 25% of the purchase price and another car for a 20% loss I f the dealer sold each car for $20000,what was the dealer's total profit or loss, in dollars for the two trans actions?
Options 1000 profit,
2000 profit,
1000 loss,
2000 loss,
3334 loss
really confused with this one and it keeps appearing frequently on GMAT PREP plz help.
For 1st car, profit = 25%
Let dealer's purchase price = x
Then x + 0.25x = 20,000
1.25x = 20,000
x = 16,000
So, profit = selling price - purchase price = 20,000 - 16,000 = $4,000

For 2nd car, loss = 20%
Let dealer's purchase price = y
Then y - 0.20y = 20,000
0.80y = 20,000
x = 25,000
So, profit = purchase price - selling price = 25,000 - 20,000 = $5,000

This means on a whole, there is a loss, which is $5,000 - $4,000 = [spoiler]$1,000[/spoiler]

The correct answer is C.
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by pemdas » Fri Jan 06, 2012 6:14 am
two different Cars
Car A sold and brings profit 25% implies Car A' cost = price of Car A/(1 +0.25)
Car B sold and brings loss 20% implies Car B's cost = price of Car B/(1-0.20)

Profit is calculated as difference between Price and Cost. If difference is positive we have profit, otherwise it's loss.

Each Car's price is 20000, hence we calculate profits realized from the sale of each Car

20000-20000/1.25
20000-20000/0.8

1/25 is 1+1/4=5/4 and 0.8 is 4/5
20000 - 4*20000/5= 4000 (multiply by reciprocal as 20000: 5/4 = 20000 *4/5)
20000 - 5*20000/4= -5000

Sum up two values: 4000-5000=-1000 implies loss of 1000 dollars
golu23 wrote:A used car dealer sold one car for a profit of 25% of the purchase price and another car for a 20% loss I f the dealer sold each car for $20000,what was the dealer's total profit or loss, in dollars for the two trans actions?
Options 1000 profit,
2000 profit,
1000 loss,
2000 loss,
3334 loss
really confused with this one and it keeps appearing frequently on GMAT PREP plz help.
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by GMATGuruNY » Fri Jan 06, 2012 8:53 am
golu23 wrote:A used car dealer sold one car for a profit of 25% of the purchase price and another car for a 20% loss I f the dealer sold each car for $20000,what was the dealer's total profit or loss, in dollars for the two trans actions?
Options 1000 profit,
2000 profit,
1000 loss,
2000 loss,
3334 loss
really confused with this one and it keeps appearing frequently on GMAT PREP plz help.
To determine the RATIO of the sum of the selling prices and to the sum of the costs, plug in easier numbers.
Let the selling price of each car = 100.

Then:
The cost of one car = 80, so that the profit = 100-80 = 20, a PROFIT of 25%.
The cost of the other car = 125, so that the loss = 125-100 = 25, a LOSS of 20%.

(Sum of the selling prices)/(sum of the costs) = (100+100)/(80+125) = 200/205 = 400/410 = 40,000/41,000.
Since the sum of the selling prices is $40,000 and the sum of the costs is $41,000, there is a LOSS of $1000.

The correct answer is C.
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by Abhishek009 » Fri Jan 06, 2012 9:07 am
golu23 wrote:A used car dealer sold one car for a profit of 25% of the purchase price and another car for a 20% loss I f the dealer sold each car for $20000,what was the dealer's total profit or loss, in dollars for the two trans actions?
Options 1000 profit,
2000 profit,
1000 loss,
2000 loss,
3334 loss
really confused with this one and it keeps appearing frequently on GMAT PREP plz help.
Let CP of the first car be 100

Selling price after a profit of 25% is 125

Hence 125 represents 20,000

Now , 1 represents 20,000/125 =>160

So, 100 represents 160*100 => 160000


For the second car -

Let CP of the car be 100

Selling price after a loss of 20% is 75

Now , 80 represents 20000

Hence 1 represents 20000/80 => 250

So , 100 represents 250*100 => 25000

Total cost price of the 2 cars is 16000+25000 = 41000

Total selling price of the 2 cars is 20000+20000 => 40000

So , Profit of 1000 is made by selling the 2 cars..
Abhishek
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