Question

The area of a rectangle gets reduced by $80$ sq units if its length is reduced by $5$ units and breadth is increased by $2$ units. If we increase the length by $10$ units and decrease the breadth by $5$ units, the area will increase by $50$ sq units. Find the length and breadth of the rectangle.

Answer 1

Let L be length of B be breadth

then,

$(L-5)(B+2)=A-80$......(1)

$(L+10)(B-5)=A+50$.....(2)

$A=L\times B$

(1) equation

$LB-5B+2L-10=A-80$

$A-5B+2L=A-70$

$2L-5B=-70$...(3)

(2) equation

$L\times B+10B-5L-50=A+50$

$10B-5L=100$

$\Rightarrow 2B-L=20$...(4)

Solving (3)& (4)

$L=40$ with $B=30$ units.

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