Car Dealership X, the total profit from sales increased by 10 percent : Problem Solving (PS)

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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: 331

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

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23 Sep 2010, 14:47

00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:14) correct

26% (02:33) wrong

based on 137 sessions

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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%

Spoiler: OA

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Joined: 02 Sep 2010

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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

onedayill wrote:

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%

Answer = C
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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:

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):

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

Answer: C.
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Joined: 25 Feb 2010

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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:

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%

Answer = C

Thanks
I got my mistake.
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Joined: 20 Jul 2010

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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%
answer C
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