Question

lenght of a room is one and a half time of its breadth. The cost of carpeting the room at rs 325 per m sq is rs 17550 and the cost of papering the walls at rs 140 per m sq is rs 24080. find the dimensions of the room.

Answer 1

here , given cost of carpeting the room = 325per m sq and it's amount is Rs. 17550.
and the cost of papering the walls = Rs. 140 per m sq is Rs. 24080.

so, we can say .......

Let the breadth of the room be b .
Then, length of the room l = 1.5 b
Area carpeted by Rs 3.25 = 1m2
area carpeted with Rs 175.50 is the area of the floor.
the area of the floor = 1/ 3.25 × 175.50 = 54 m².

therefore lb=54
(1.5b)×b=54

1.5b² = 54
b² = 54 / 1.5 = 36
b = 6 m

therefore the breadth of the room is 6 m.
length of the room =1.5×6= 9 m
let the height of the room be h m.

area of the walls = 2h + ( l+ b) = 2h ( 9+6) = 30h m².
since 1 door and 2 windows occupy 8 meter square.
therefore area of papering =30h-8 meter square......(1)

cost of papering the walls at Rs. 1.40 per m2 is Rs. 240.80.
therefore area of papering = 240.80 / 1.40 = 172m².

from the (1)........ we get,

30h -8= 172
30h = 180
h = 180/30
h= 6 m.

therefore, we can say that the height of the room is 6 m.and
hence, the dimensions of the room is 9×6×6mtr.


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