If length of rectangle is decreased by $5 m$ and breadth is increased by $3 m$ then its area reduces $9$ Sq.m. If length and breadth increased by $3 m$ and $2 m$ respectively, then its are increased by $67 s q . m$ . What is the length of rectangle?

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Solution

Let length and breadth of the rectangle is $x$ and $y$ ,
Then as per first condition ,
$(x - 5) (y + 3) = x y - 9$
$x y - 5 y + 3 x - 15 = x y - 9$
$3 x - 5 y = 6$ $- - - - - (1)$
As per second condition,
$(x + 3) (y + 2) = x y + 67$
$x y + 3 y + 2 x + 6 = x y + 67$
$2 x + 3 y = 61$ $- - - - - (2)$
On multiplying equation $(1)$ by $3$ and equation $(2)$ by $5$ then adding, we get
$9 x - 15 y = 18$
$10 x + 15 y = 305$
$- - - - - - - - - -$
$19 x = 323$
$∴ x = 17$
Hence, the length of the rectangle is $17 m$ .

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If length of rectangle is decreased by 5m and breadth is increased by 3m then its area reduces 9 Sq.m. If length and breadth increased by 3m and 2m respectively, then its are increased by 67sq.m. What is the length of rectangle?

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