The length of a rectangular plot is increased by 10%. To keep its area

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

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


Rest At the End, Not in the Middle
- Kobe Bryant

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