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# If the value of a piece of property decreases by 10 percent while the

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Math Expert
Joined: 02 Sep 2009
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If the value of a piece of property decreases by 10 percent while the  [#permalink]

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01 Feb 2018, 23:35
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Difficulty:

45% (medium)

Question Stats:

52% (01:51) correct 48% (01:45) wrong based on 27 sessions

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If the value of a piece of property decreases by 10 percent while the new tax rate on the property represents 110% of the original tax rate, what is the effect on the taxes?

(A) Taxes increase by 10 percent.
(B) Taxes increase by 1 percent.
(C) There is no change in taxes.
(D) Taxes decrease by 1 percent.
(E) Taxes decrease by 10 percent.

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Re: If the value of a piece of property decreases by 10 percent while the  [#permalink]

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01 Feb 2018, 23:53
Option D

let the property value be 100 and tax be 100. Total tax = 100*100 = 10000

Now the property value decreases by 10%. Hence new value = 100*90/100 = 90.

Also tax becomes 110%. Hence new tax = 110/100*100 = 110.

Hence total tax = 90*110= 9900

Hence there is a decrease of (10000-9900)/10000 = 0.01 = 1%
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02 Feb 2018, 12:15
Bunuel wrote:
If the value of a piece of property decreases by 10 percent while the new tax rate on the property represents 110% of the original tax rate, what is the effect on the taxes?

(A) Taxes increase by 10 percent.
(B) Taxes increase by 1 percent.
(C) There is no change in taxes.
(D) Taxes decrease by 1 percent.
(E) Taxes decrease by 10 percent.

Multipliers and algebra
Let (1)P = property's value
Let (1)T = tax rate

Original tax amount=(property value)*(tax rate)
Original tax amount: $$P*T = PT$$

New tax amount:(new property value)*(new tax rate)
New property value: $$.90P$$ (10 percent decrease)
New tax rate: $$1.10T$$ (10 percent increase)
New tax amount: $$.90P*1.1T =.99 PT$$

Percent change: $$\frac{New-Old}{Old} * 100$$

$$\frac{.99PT-1PT}{1PT}*100=\frac{-.01}{1}*100= -.01*100 =$$

-1 percent (Minus sign = percent decrease)

Tax amount decreases by 1 percent

Assign values
In this problem, "taxes" might be a subtle word for some people.
"Taxes" = tax amount, and
Tax amount = (Property value)*(tax rate)

Let original property value = $1,000 Let original tax rate = 10 percent = .10 Original "taxes" (tax amount):($1,000*.10) = $100 New property value = original decreased by 10% = 90% of original value New property value: (.90 *$1,000) = \$900
New tax rate, increased by 10 percent, = 110% of original tax rate:
New tax rate: $$1.1(.10) = .11$$
New tax amount: $$900*(.11) = 99$$

Percent increase or decrease in tax amount?

$$\frac{New-Old}{Old} * 100$$

$$\frac{99-100}{100}*100= \frac{-1}{100}*100 = -.01*100=$$

-1 percent

Tax amount decreases by 1 percent

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If the value of a piece of property decreases by 10 percent while the   [#permalink] 02 Feb 2018, 12:15
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