Question

The length ofa given rectangle is increased by 20% and the breadth is decreased by 20%, then the area

• A. remains the same
• B. increases by 5%
• C. decreases by 5%
• D. decreases by 4%

Answer 1

The correct option is D decreases by 4%

Let the original length and breadth be $l$ and $b$, respectively.

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

Since,

New length $=l+\frac{l}{5}=\frac{6l}{5}$

New breadth $=b-\frac{b}{5}=\frac{4b}{5}$

Therefore, new area will be

$=\frac{24lb}{25}$

Therefore, the area of rectangle is decreased

$=\frac{lb-\frac{24lb}{25}}{lw}\times 100$

$=\frac{1}{25}\times 100$

$=4\%$

Hence, the area is decreased by $4\%$.