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The length of a rectangle is decreased by 15% and its width is increas

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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 17 Jan 2016, 09:10
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The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%

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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 17 Jan 2016, 09:41
Let the length of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 18 Jan 2016, 22:35
Hi All,

This question can be solved in a variety of different ways, including various algebraic approaches and TESTing VALUES. Here's how you can use fractions to your advantage and save some time.

We're told that the length of a rectangle is decreased by 15% and its width is increased by 40%. We're asked if the area of the rectangle decreases or increases and by what percent.

The original area of the rectangle can be written as...

(L)(W) = Area

The two changes can be written as:
15% decrease = 8.5/10
40% increase = 14/10

After the changes occur, we have...

(8.5/10)(L)(14/10)(W) =
(8.5/10)(14/10)(L)(W) =
(8.5)(14)/100 x (L)(W) =
119/100 x (L)(W)

119/100 = a 19% increase

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 13 May 2017, 08:07
1
We can also solve this by using the formula

a+b+(a*b)/100
=(-15)+(40)+(-15*40)/100
=25-6
=19%
which is positive so it represents a 19% increase.
D is the answer
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 15 May 2017, 23:40
Let the original length be 20 ; and width = 10
original area = 20 * 10 = 200

New length = .85 * 20 = 17
New width = 1.40 * 10 = 14

new area = 17 * 14 = 238

% increase =\(\frac{38}{200} * 100\) = 19%

Ans: D
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 16 May 2017, 01:29
Let original length= L; original width= W
New length= 0.85L; New width= 1.4W

Original Area= LW
New Area= 0.85L*1.4W= 1.19LW

Change in Area= 1.19LW-LW= 0.19LW
Percentage increase= \(\frac{0.19LW}{LW}\)*100= 19%

Answer: D.

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 16 May 2017, 02:28
Simplest Way:-
New Length : 0.85L (L= Original length)
New Width : 1.4W (L= Original width)
Therefore New Area= 0.85*1.4*L*W=1.19LW implies 19%Increase.

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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 16 May 2017, 10:19
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Bunuel wrote:
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%


\(-15 + 40 +\frac{(-15)(40)}{100}\)

\(= 25 - 6\)

\(= 19\)

Thus, there will be an increase in area by (D) 19%
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The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 16 May 2017, 19:05
Abhishek009 wrote:
Bunuel wrote:
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%


\(-15 + 40 +\frac{(-15)(40)}{100}\)

\(= 25 - 6\)

\(= 19\)

Thus, there will be an increase in area by (D) 19%



Hi Abhishek,

Please explain above approach. Is this approach applicable for all % increase or % decrease problems ?

How will you identify that 19 is increase or decrease % ?

thanks
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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New post 19 May 2017, 05:19
Bunuel wrote:
The length of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?

A. Decreases by 19%
B. Decreases by 25%
C. Increases by 6%
D. Increases by 19%
E. Increases by 25%


We can let the original length of the rectangle = x and the original width of the rectangle = y. Thus, the original area is xy.

When the length decreases by 15%, the new length is 0.85x, and when the width increases by 40%, the new width is 1.4y. Thus, the new area is (0.85x)(1.4y) = 1.19xy.

We can use the percent change formula: (New Value - Old Value)/Old Value x 100%. Thus, the area changes by (1.19xy - xy)/xy = 0.19xy/xy = 0.19 = 19%. This value is positive, indicating an increase.

Answer: D
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Re: The length of a rectangle is decreased by 15% and its width is increas  [#permalink]

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