Question

If the length of a rectangle is increased by $\frac{1}{3}$ rd and the width is decreased by $\frac{1}{3}$ rd, then the area of the rectangle is decreased by the fraction

• A. 2/3
• B. 1/6
• C. 1/9
• D. 1/8

Answer 1

The correct option is C 1/9

Let the original length and width be $l$ and $w$, respectively.

So, the area of rectangle $=lw$ $.......\left(1\right)$

Since, \

New length $=l+\frac{l}{3}=\frac{4l}{3}$

New width $=w-\frac{w}{3}=\frac{2w}{3}$

Therefore, new area will be

$=\frac{8lw}{9}$

Therefore, the area of rectangle is decreased

$=lw-\frac{8lw}{9}$

$=\frac{lw}{9}$

Hence, $\frac{1}{9}$ is the answer.