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# The difference between the value of a number increased by 25

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Joined: 07 Feb 2010
Posts: 112
The difference between the value of a number increased by 25  [#permalink]

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20 Dec 2010, 08:11
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85% (01:33) correct 15% (02:14) wrong based on 182 sessions

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The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90
Math Expert
Joined: 02 Sep 2009
Posts: 62499
Re: the differance between the value of a number  [#permalink]

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20 Dec 2010, 08:15
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anilnandyala wrote:
the differance between the value of a number increased by 25% and the value of the original number decreased by 30% is 22 what is the original number?

40
50
65
70
90

Let the original # be $$x$$ then $$1.25x-0.7x=22$$ --> $$x=40$$.

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Re: The difference between the value of a number increased by 25  [#permalink]

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30 Mar 2017, 08:01
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anilnandyala wrote:
The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90

Let x = the original number

Value of the number INCREASED by 25% = 1.25x
Value of the number DECREASED by 30% = 0.7x

DIFFERENCE = 22
So, 1.25x - 0.7x = 22
Simplify: 0.55x = 22
So, x = 22/0.55

NOTE: We need not calculate 22/0.55
Notice that 22/0.5 = 44
Since 0.55 is a little bit BIGGER than 0.5, we can conclude that 22/0.55 will be a little bit SMALLER than 44

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Re: The difference between the value of a number increased by 25  [#permalink]

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17 May 2017, 13:37
The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90

Let the number be x.
Number increased by 25% = 125% of x = 1.25x
Original number decreased by 30% = 70% of x = 0.7x
Difference between values = 1.25x - 0.7x = 22, 0.55x = 22
x = 22/0.55 = 40

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Re: The difference between the value of a number increased by 25  [#permalink]

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19 Oct 2018, 14:20
anilnandyala wrote:
The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90

We can let n = the original number and create the equation:

1.25n - 0.7n = 22

0.55n = 22

n = 40

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Re: The difference between the value of a number increased by 25  [#permalink]

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09 Jan 2020, 08:17
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Re: The difference between the value of a number increased by 25   [#permalink] 09 Jan 2020, 08:17
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