The area of the four walls of a room is 1080 sq.ft. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth are in the ratio 4 : 5. What is the area of the roof?
- 240 sq.ft.
- 450 sq.ft.
- 540 sq.ft.
- 720 sq.ft.
- Cannot be determined
The Usual Method
Let the height and breadth of the room be 2x and 5x respectively.
Similarly let the height and breadth of the room be 4y and 5y respectively.
Area of the walls = length x height x 2 + breadth x height x 2 = 1080
Also note that height of the room is constant, so:
Substituting this in Eq. 1, we get:
Hence, length of room = ft
And breadth of room = ft
Hence area of roof = 30 x 15 = 450 sq.ft.
Estimated Time to arrive at the answer = 90 seconds.
Ratio of height to length = 2 : 5 = 4 : 10
Ratio of height to breadth = 4 : 5
Thus ratio of length to breadth = 10 : 5
Hence, area of ceiling =
Hence, the area of the ceiling should be a multiple of 50. The only option satisfying this condition is option ‘2’.
Estimated Time to arrive at the answer = 10 seconds.