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Question

A room is half as long as it is broad. The cost of carpeting the room at Rs 3.25m2 is Rs 175.50 and the cost of preparing the walls at Rs1.40 per sq.m is Rs240.80. If 1 door and 2 windows occupy 8m2, then find the dimensions of the room ?

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Solution

Let the breadth of the room be am
Length of the room=a+a2=3a2m
Area of the rooma×3a2=3a22sq.m
Cost of carpeting the room at Rs.3.25per sq.m=Rs.3.25×3a22
75.50=3.25×3a22
a2=175.50×23.25×3=36
a=6
Breadth=a=6m and length=3×62=9m
Let the height of the room be hm
Area of 4 walls=2(l+b)×h=2(6+9)×h=30hsq.m
Area of 1 door and 2 windows=8sq.m
Area to be papered=Area of 4 wallsArea of 1 door and 2 windows
=(30h8)sq.m
Cost of papering walls at Rs.1.40per sq.m=Rs.(30h8)×1.40
240.80=(30h8)×1.40
30h8=240.801.40=172
30h=172+8=180
h=18030=6m
Hence, dimensions of the room are
Length=9m, Breadth=6m and Height=6m

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