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Get access to the detailed solutions to the previous years questions asked in CMAT exam.
Let the breadth (b) of the room be 'x' metres.
then, length (I) of the room = x + 2 metres.
Area (A) = l x b = x(x +2) m2
Given, length is increased by 4 meters and the breadth decreased by 2 meters
Then, new length(l') of the room = x+6 metres
new breadth(b') of the room = x-2 metres
New Area(A') of the room = l' x b' = (x + 6) (x - 2) m2
Also given that A = A'
⇒ x(x + 2) = (x + 6)(x − 2)
⇒ x2 + 2x = x2 + 4x − 12
⇒ 2x = 12
⇒ x = 6
Therefore the length of the room (l) = 8 metres
and breadth of the room (b) = 6 metres
and given height of the room (h) = 3 metres
Since the room will be in the shape of a cuboid, Surface area = 2(l x b + b x h + l x h)
But the Surface area of Walls = Total Surface area - Area of Roof and Floor = 2(l x b - b x h + l x h) - 2(l x b) = 2(8 x 3 + 6 x 3) = 84m2