Question

What change in percent is made in the area of a rectangle by decreasing its length and increasing its breadth by $5\%$?

• A. $2.5\%$ increase
• B. $0.35\%$ increase
• C. $0.25\%$ decrease
• D. $2.5\%$ decrease

Answer 1

Answer: (C)

$0.25\%$ decrease

Let the length of rectangle be $L$ and breadth be $B$.

$\therefore$ Area = $LB$

NOW,

After decreasing the length of rectangle by $5\%$ and Increasing the breadth by $5\%$

Decreased length $=\frac{95}{100}L$.

&Increased breadth $=\frac{105}{100}B$.

$\therefore$ Area of this newly formed rectangle $=\frac{95}{100}L\times \frac{105}{100}B$

$=0.9975LB$

Now,

Decrease in Area $=(1-0.9975)LB$

$=0.0025LB$

$\therefore \%$ Decrease in Area $=\frac{0.0025LB}{LB}\times 100$

$=0.25\%$