CMAT 2018 - Slot 2 Quantitative Aptitude Question 2
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Quantitative Aptitude
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