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# parking garage

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parking garage [#permalink]  30 Oct 2009, 15:24
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A particular parking garage is increasing its rates by 15 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?

Looking for easy ways to solve this problem..
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Re: parking garage [#permalink]  30 Oct 2009, 15:52
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is 13% the answer?

let m be the rate per month , then 1.15m is the rate per month after increase

let d be the number of days he used garage, then total cost assuming 30 days in month = md/30

let n be days to be reduced to remain at same cost, so we get

we need to find n*100/d

md/30 = 1.15m (d-n)/30

==>

d = 1.15(d-n)

divide both sides by d ==>
1 = 1.15 - 1.15n/d
==>1.15n/d = .15
==>100n/d = 15/1.15 = 13
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Re: parking garage [#permalink]  30 Oct 2009, 21:13
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I got 13 too, thanks sri and others for explanations
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Re: parking garage [#permalink]  13 Aug 2010, 06:45
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Best way to solve such Questions:

Remember - If Value of an item goes UP by x%, then the REDUCTION to be made to bring it to original value is calculated by formula:

x*100/(100+x)%

If Value of an item goes DOWN by x%, then the INCREMENT to be made to bring it to original value is calculated by formula:

x*100/(100-x)%

Hope this helps!
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Re: parking garage [#permalink]  30 Oct 2009, 16:48
Assuming Current Cost of $1, next month it will cost$1.15 for same services

X * 1.15 = \$1 with X being the percentage of full previous services

X = 86.956% so you must use roughly 13% less at the higher rate to keep your costs the same.

Note if it asked you in Month 3 or X amount of decrease, you would just compound this rate.

Ex. .86956 ^2 = Usage in Month 3 or just 1 / 1.15^2
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Re: parking garage [#permalink]  30 Oct 2009, 17:01
R*D=E
1.15R*(1-x)D=E
R*D=1.15R*(1-x)D
1-\frac{1}{1.15}=x

Solving, x=13%
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Re: parking garage [#permalink]  17 Nov 2009, 04:19
Let parking rate = 100

=(15/100+15)*100
=13.04%
Re: parking garage   [#permalink] 17 Nov 2009, 04:19
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