Question

The area of a rectangle gets reduced by $9$ sq. units, if its length is reduced by $5$ units and the breadth, is increased by $3$ units. If we increase the length by $3$ units and breadth by $2$ units, the area is increased by $67$ sq. units. Find the length and breadth of the rectangle.

• A. length $=12$, breadth $=6$
• B. length $=20$, breadth $=15$
• C. length $=17$, breadth $=9$
• D. length $=21$, breadth $=8$

Answer 1

The correct option is C length $=17$, breadth $=9$

Let the length and breadth of the rectangle be $x$ and $y$.
$\therefore$ Area of rectangle $=xy$

According to given condition:

$(x-5)(y+3)=xy-9$
$\therefore xy+3x-5y-15=xy-9\Rightarrow 3x-5y=6$ ....$\left(i\right)$

and
$(x+3)(y+2)=xy+67$
$\therefore xy+2x+3y+6=xy+67\Rightarrow 2x+3y=61$ .....$\left(ii\right)$

On multiplying equation $\left(i\right)$ by $2$, we get,
$6x-10y=12$ ....$\left(iii\right)$

On multiplying equation $\left(ii\right)$ by $3$, we get,
$6x+9y=183$ .....$\left(iv\right)$

On subtracting $\left(iv\right)$ from $\left(iii\right)$, we get,
$-19y=-171\Rightarrow y=9$

by putting $y=9$ in $\left(i\right)$. we get,
$3x-5\left(9\right)=6\Rightarrow x=17$

$\therefore$ length $=17$ and breadth $=9$