If the length of a rectangle is increased by 10% and the area is unchanged , then its corresponding breadth must be decreased by? Choose the correct option:
A) 9 1 / 19 B) 9 1 / 15 C) 9 1 / 16 D) 9 1 / 11 E) 9 1 / 10

Rationale: suppose length = 100 m and breadth = x m area = 100 m new length = 110 m and breadth = ( x - y % of x ) then , \ inline 110 \ times ( x - \ frac { y } { 100 } x ) = 100 \ times x \ inline \ rightarrow \ inline 110 \ times ( 1 - \ frac { y } { 100 } ) = 100 \ inline \ rightarrow \ inline 1 - \ frac { y } { 100 } = \ frac { 100 } { 110 } \ inline \ rightarrow \ frac { y } { 100 } = 1 - \ frac { 100 } { 110 } = \ frac { 1 } { 11 } \ inline y = \ frac { 100 } { 11 } = 9 \ frac { 1 } { 10 } % answer : e
Answer: E