Percentage changes

Question

Jack sold two used cars for 60'000 SEK each.
He made a 20% profit on the first one, but a 20% loss on the second one.
Did he make a profit or a loss with the business?

Answer 1

20% profit means 1.2X = $60,000

x = $50,000 is what he paid for the car

 

20% loss means .8y = $60,000

y = $75,000 is what he paid for the car

 

Total cost is $75,000 + $50,000 = $125,000

Total sale is $60,000 + $60,000 = $120,000

 

Therefore he lost $5,000

Answer 2

Car 1, selling price p1, Car 2, selling price p2.  p1+p2 = 60000

 

20% profit on Car1 means actual price (100) p1/ (120).  (If the car sold at 120, say, then the actual price is 100, take the ratio and multiply by p1))  Similarly, 20% loss on Car 2 means its actual price is (80) p2 / (100)  (If the car sold at 100, say,  then the actual price is 80, take the ratio and multiply by p2)) .

 

So the actual price for both cars is (0.8333)p1 + (0.8) p2.  Use p1 +  p2 = 60000.

 

Actual price = (0.8333)p1 + (0.8)(60000 - p1) = (0.0333)p1 + 48000.

 

Look at the ratio r = 60000 / [(0.0333)p1 + 48000]   DEPENDS ON p1, FREDERICK.

If r > 1 there was profit (total actual price was smaller than the total selling price)

 

If r < 1, there was loss (total actual price was greater than the total selling price)

If r = 1, no loss, no profit.

 

Dr. G.