If the width of a rectangular plot is increased by one-fourth and the : Problem Solving (PS)

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If the width of a rectangular plot is increased by one-fourth and the

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Math Expert

Joined: 02 Sep 2009

Posts: 53063

If the width of a rectangular plot is increased by one-fourth and the [#permalink]

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04 Sep 2018, 23:28

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Question Stats:

100% (01:14) correct

0% (00:00) wrong

based on 29 sessions

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If the width of a rectangular plot is increased by one-fourth and the length is decreased by one-fifth, then the area will be increased by

A. 0%
B. 5%
C 10%
D. 12%
E. 15%

Spoiler: OA

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Re: If the width of a rectangular plot is increased by one-fourth and the [#permalink]

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05 Sep 2018, 00:54

Bunuel wrote:

If the width of a rectangular plot is increased by one-fourth and the length is decreased by one-fifth, then the area will be increased by

A. 0%
B. 5%
C 10%
D. 12%
E. 15%

Increases width=\(w(1+\frac{1}{4})=\frac{5}{4}w\)
Decreased length=\(l(1-\frac{1}{5})=\frac{4}{5}l\)

New Area=\(\frac{5}{4}w*\frac{4}{5}l\)=lw

Change in area=0%

Ans. (A)
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Re: If the width of a rectangular plot is increased by one-fourth and the [#permalink]

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05 Sep 2018, 03:28

Let's test numbers here.

(1) Assuming the initial plot's length=10 and width=10, its area equals 10*10=100
(2) To increase the width by a fourth, we multiply 10*1.25 to yield a total of 12.5
(3) To decrease the length by a fifth, we multiply 10*0.8 to yield a total of 8
(4) We then calculate the area of the second plot, 12.5*8=100, which is the same as the initial plot!

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Re: If the width of a rectangular plot is increased by one-fourth and the [#permalink]

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05 Sep 2018, 06:49

Bunuel wrote:

If the width of a rectangular plot is increased by one-fourth and the length is decreased by one-fifth, then the area will be increased by

A. 0%
B. 5%
C 10%
D. 12%
E. 15%

Let original Length be \(5\) and Breadth be \(4\) , So Area is \(20\)

Changed Dimension of the Rectangle are Length = \(4\) and Breadth = \(5\) , So Area = \(20\)

Since there is no change in area , the answer must be (A)

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