Question

If the length is increased by 3 cm and the breadth is increased by 2 cm, the area of a rectangle increases by 67 cm2.But, if the length is reduced by 5 cm and the breadth is increased by 3 cm, the area reduces by 9 cm2.Find the area of the rectangle (in cm2). 156 149 176 150 153

Solution

The correct option is E 153 Let the length of rectangle = x cmThe breadth of rectangle = y cm and Area = xy cm2.∴ As given in the problem,(x+3)(y+2)=xy+67or     2x+3y=61..................(i)Also,(x−5)(y+3)=xy−9or  3x−5y=6................(ii){2x+3y=61........(i)×33x−5y=6........(ii)×2On  solving,or y=17119=9On putting, y=9 in (i), we have2x+27=61or x=17 cm and y = 9 cmArea=xy=17×9=153 cm2

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