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In measuring the sides of a rectangle, one side

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Intern
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Joined: 25 Jan 2013
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In measuring the sides of a rectangle, one side [#permalink] New post 20 Feb 2013, 21:02
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E

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Question Stats:

84% (01:52) correct 15% (00:33) wrong based on 26 sessions
In measuring the sides of a rectangle, one side is taken 8% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.

A. 3.5%
B. 2.4%
C. 3%
D. 5%
E. 2.6%
[Reveal] Spoiler: OA
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Re: In measuring the sides of a rectangle, one side [#permalink] New post 20 Feb 2013, 21:43
antoxavier wrote:
In measuring the sides of a rectangle, one side is taken 8% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.

A. 3.5%
B. 2.4%
C. 3%
D. 5%
E. 2.6%


Let the sides of the rectangle be a and b.

actual area of the rectangle without error = ab

New side a ( 8% in excess) = a+0.08a = 1.08a
New side b ( 5% in deficit) = b-0.05b = 0.95b

Area of the new rectangle = (1.08a)(0.95b)= (1.0260)ab
say a=1 and b=1
area of the original rectangle = 1
area of the new rectangle = 1.026
change in the area calculation = .026
error percentage in the area calculated = 2.6%

Let me know otherwise.
Cheers
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Re: In measuring the sides of a rectangle, one side [#permalink] New post 21 Feb 2013, 02:36
Expert's post
antoxavier wrote:
In measuring the sides of a rectangle, one side is taken 8% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.

A. 3.5%
B. 2.4%
C. 3%
D. 5%
E. 2.6%


Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.

Now, the area obtained with wrong measurements would be 108*95=10,260, which is 2.6% greater than the actual area.

Answer: E.
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Re: In measuring the sides of a rectangle, one side   [#permalink] 21 Feb 2013, 02:36
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