Problem Solving

The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]

Answer is E.

Let initial length be l and width be b.
let x be the decrease in percentage of the width.

l * b = (l+0.25l) * (b-xb)

l*b = l*b + 0.25lb - 1.25lxb

==> 0.25lb = 1.25lxb
==> x= 0.25/1.25 = 0.2

Therefore the decrease in width should be 20%

sanju09 wrote:The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]

It is always good to use numbers to make the calculations easier:

In the current problem let us consider l=4 and b=3, Area= 12.

Now if we are to increase l by 25% then l=5 and b=? according to the problem statement.

since area should be equal for the two: 4*3=5*x

resulting in x (new width)=2.4

2.4 is 80% of the original value 3, Hence we have to decrease the original width by 20%, Answer E

sanju09 wrote:The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]

We can use logic/common sense/GMAT knowledge to answer this question in under 15 seconds.

First, if we increase one dimension, we need to decrease the other to keep area constant: eliminate A, B and D.

Second, there's no way that the percentage decrease will be the same as the percentage increase (a common GMAT trap is answers that just repeat numbers from the question stem): eliminate C.

Choose E (without doing any math)!

* * *

If for some reason you do want to do math, then:

l*w = (5/4)l * (x)w

1 = (5/4)(x)

4/5 = x

So, width gets decreased by 1 - 4/5 = 1/5

boss take lenght 100 and width 20 and solve the problem

pradeepkaushal9518 wrote:boss take lenght 100 and width 20 and solve the problem

why not take both 100, btw Stuart Kovinsky's logical approach serves the best when time is the limiting factor, eliminate as much as you can to avoid doing math where it's really not required

Stuart Kovinsky wrote:

sanju09 wrote:The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be:
A. kept unchanged.
B. increased by 25%.
C. reduced by 25%.
D. increased by 20%.
E. reduced by 20%.

[spoiler]Source: winningprep.com[/spoiler]

We can use logic/common sense/GMAT knowledge to answer this question in under 15 seconds.

First, if we increase one dimension, we need to decrease the other to keep area constant: eliminate A, B and D.

Second, there's no way that the percentage decrease will be the same as the percentage increase (a common GMAT trap is answers that just repeat numbers from the question stem): eliminate C.

Choose E (without doing any math)!

* * *

If for some reason you do want to do math, then:

l*w = (5/4)l * (x)w

1 = (5/4)(x)

4/5 = x

So, width gets decreased by 1 - 4/5 = 1/5

wonderful explanation!!!
In a hurry to solve problems ,I tend to overlook such problems which needs common sense approach.
Thanks Stuart