The area of a rectangle is reduced by 25 square units if its length is increased by 5 units and breadth is decreased by 3 units. If we increase length by 2 units and breadth by 5 units, area is increased by 285 square units. Find the dimension of the rectangle.
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Let length be x
Breadth be y
Area = xy sq units
A/q
(x+5)(y-3) = xy - 25
⇒xy -3x +5y -15 = xy -25
⇒3x -5y =10_____(1)
Also, (x+2)(y+5) = xy + 285
⇒xy + 5x+2y +10 = xy +285
⇒5x+2y = 275____(2)
Multiplying equation (1) by 2 and (2) by 5 and adding,
6x+25x = 20 + 1375
⇒31x = 1395
⇒x = 45 units
so, 5y =135-10 = 125
⇒y = 25 units
Breadth be y
Area = xy sq units
A/q
(x+5)(y-3) = xy - 25
⇒xy -3x +5y -15 = xy -25
⇒3x -5y =10_____(1)
Also, (x+2)(y+5) = xy + 285
⇒xy + 5x+2y +10 = xy +285
⇒5x+2y = 275____(2)
Multiplying equation (1) by 2 and (2) by 5 and adding,
6x+25x = 20 + 1375
⇒31x = 1395
⇒x = 45 units
so, 5y =135-10 = 125
⇒y = 25 units
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