Question

A cuboid room is 1 and half as long as it's broad. The cost of carpeting the room at the rate of Rs.5/sq.m is Rs.480 and the cost of papering the walls with coloured paper at the rate of Rs 3/sq.m is Rs.360.Find the dimensions of the room.

Answer 1

let the breadth be x.
then length = 3/2x
area of floor = l*b = x*3/2*x = 3/2*$x^{2}$
cost of carpeting = rate * area 
480 = 5*3/2*$x^{2}$
$x^{2}$ = 480*2/3*2= 64
x= 8
b = 8
l = 3/2*8 = 12
lateral surface area of the room = 2h(l+b) = 2*h*(12+8) = 2*h*20 = 40h
cost of papering = rate * lateral surface area
360 = 3*40h
h = 360/(40*3) = 360/120 = 3
therefore dimensions of the room are : 
Length = 12 m
Breadth = 8 m
Height = 3 m
Inform me if I am wrong.