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

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Senior Manager
Joined: 25 Feb 2010
Posts: 461
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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Question Stats:

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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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Joined: 02 Sep 2010
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Location: London
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
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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Posts: 461
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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Joined: 20 Jul 2010
Posts: 263
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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Posts: 16014
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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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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