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Car Dealership X, the total profit from sales increased by 10 percent

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Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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23 Sep 2010, 14:47
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Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.

A. 18%
B. 20%
C. 22%
D. 23%
E. 25%
[Reveal] Spoiler: OA

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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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23 Sep 2010, 14:52
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onedayill wrote:
Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.

18%
20%
22%
23%
25%

Let Profit be x and cars sold be y

Originally Profit/Car = x/y

Now it is 1.1x / 0.9 y = 11/9 (x/y)

Increase in profit per car = ((2/9) (x/y)) / (x/y) * 100 = 22.22%

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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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23 Sep 2010, 14:59
Expert's post
onedayill wrote:
Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.

18%
20%
22%
23%
25%

Let the initial profit be $$p$$ and initial number of cars sold be $$n$$ --> initial profit per car would be $$\frac{p}{n}$$;

After 1 year profit per car would be $$\frac{1.1p}{0.9n}\approx{1.22*\frac{p}{n}}$$;

General formula for percent increase or decrease, (percent change):

$$Percent \ change=\frac{Change}{Original}*100=\frac{1.22*\frac{p}{n}-\frac{p}{n}}{\frac{p}{n}}*100=22$$.

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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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23 Sep 2010, 15:00
shrouded1 wrote:
onedayill wrote:
Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.

18%
20%
22%
23%
25%

Let Profit be x and cars sold be y

Originally Profit/Car = x/y

Now it is 1.1x / 0.9 y = 11/9 (x/y)

Increase in profit per car = ((2/9) (x/y)) / (x/y) * 100 = 22.22%

Thanks
I got my mistake.
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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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23 Sep 2010, 20:52
I did this by putting numbers, I don't know if this approach is correct.

Previous Years - Number of cars be 10 , total profit be 100....

this year - Number of cars will be 9 , total profit will be 110..

Previous year ---- profit per car = 100/10 = 10
this year profit = 110/9 = 12.2
percent increase = 22%
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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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23 Sep 2010, 22:19
What is true in general will also be true in particular

Substituting numbers is perfectly fine
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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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15 Dec 2015, 01:31
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Re: Car Dealership X, the total profit from sales increased by 10 percent [#permalink]

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10 Apr 2016, 15:40
(1.1p/.9c)/(p/c)=1.22=22% increase
Re: Car Dealership X, the total profit from sales increased by 10 percent   [#permalink] 10 Apr 2016, 15:40
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