Question

The length of a room is $30$ m. The ratio of its length to its breadth is $3:2$. If this ratio had been equal to $5:3$, then what is the difference between the two areas of the rectangle?

• A.
  $40$ sq m
• B.
  $60$ sq m
• C.
  $80$ sq m
• D.
  $100$ sq m

Answer 1

The correct option is B

$60$ sq m
Let the breadth be $b$

Given,
$30:b$ is $3:2$
$\Rightarrow$ $\frac{30}{b}=\frac{3}{2}$
$\Rightarrow 3b=60$
$\Rightarrow b=20$

$\therefore$ Old area $=$ $30\times 20=600$ sq m.
New ratio $=5:3$
$30:b$ is $5:3$
$\Rightarrow$ $\frac{30}{b}=\frac{5}{3}$
$\Rightarrow 5b=90$
$\Rightarrow b=18$

$\therefore$ New area $=$ $30\times 18=540$ sq m.

$\therefore$ Difference in areas $=600-540=60$ sq m