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The length of a rectangular plot is increased by 10%. To keep its area 27 Jan 2021, 05:00
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D
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25% (medium)

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72% (01:25) correct 28% (01:30) wrong based on 86 sessions

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The length of a rectangular plot is increased by 10%. To keep its area unchanged, the width of the plot should be:

(A) Kept unchanged
(B) Increased by 10%
(C) Increased by \(9 \frac{1}{11}\)%
(D) Reduced by \(9 \frac{1}{11}\)%.
(E) Reduced by 10%.
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D
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The length of a rectangular plot is increased by 10%. To keep its area 27 Jan 2021, 05:51
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10% Increase the reduction should be 9.0909%

Ans D
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The length of a rectangular plot is increased by 10%. To keep its area 17 Mar 2021, 23:37
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let initial l=10 and b=10 area 100
then new length 11 and breadth = x
so 11x=100
new x =100/11
percentage reduction ((10-100/11)/10)x100
hence the answer d
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The length of a rectangular plot is increased by 10%. To keep its area Updated on: 04 Jun 2021, 02:59
Originally posted by Jainam24 on 04 Jun 2021, 00:22.
Last edited by Jainam24 on 04 Jun 2021, 02:59, edited 1 time in total.
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My approach was to go about eliminate options. This saved considerable time. I was done solving in 23 seconds!

A, B and C are incorrect as the length has increased, the width has to decrease to make the area equal.

We are left with options D and E.

E is incorrect as an increase in area doesn't need an equal decrease in area in % terms.
Why? Since the base value has increased, it needs a smaller % to compensate.

E.g. Price of a choclate increased by 10%. Earlier it was worth 100 bucks. So now it becomes worth 110. However now if the price becomes 100 bucks, the % decrease isn't 10% it is 9.09% as the base has increased to 110 and thus a smaller % is need for compensation

Option D is the answer


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The length of a rectangular plot is increased by 10%. To keep its area 04 Jun 2021, 01:19
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Solution:

For two quantities that are inversely related to each other, if there is an increase of x/y in one of the values there is a corresponding decrease of x/(x+y) in the other and if there is a decrease of x/y in one of the values there is a decrease of x/(|y-x)| on the other.

So here, there is an increase in the plot length by 10% which is 1/10 as a fraction( x=1 and y=10)

Length and breadth are inversely related when area is constant = > Breadth decreases by x/(x+y)

= 1/(1+10) =1/11 as a fraction that is 9.09 as a percentage . (option c)

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The length of a rectangular plot is increased by 10%. To keep its area 04 Jun 2021, 01:22
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Let length be 10 and width be 11.

Area = 10 * 11 = 110

Length increased by 10%. Therefore new length: \(\frac{110}{100} * 10 = 11\)

Now for the area to be 110, the width should be 10.

Percent change in width: \(\frac{10 - 11 }{ 11} * 100\) = - 9.99% [minus sign shows decrease].

Answer D
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