Question

the length of a room is 50 per cent more than its breadth. The cost of carpeting the room at the rate of Rs. 38.50m^2 is Rs. 924 and the cost of painting the walls at the rate of Rs. 5.50 per m^2 is Rs. 1320. Find the dimension of the room

Answer 1

Let the length of room be a
Width = a + a/2 = 3a/2

Cost of carpeting = 924
Rate of carpeting = 38.5

Area of floor = Cost /Rate
= 924 / 38.5
= 24 m^2

Length *Width = 24 m^2
a*3a/2 = 24
=> 3a^2 = 48
=> a^2 = 16
=> a= 4 m

Length of room = 4 m
Width of room = 6 m

Now,

Cost of painting =1320
Rate of painting = 5.5

Area of four walls = Cost /Rate
=>2(Length +width) *Height = 1320/5.5
=> 2*10 * Height = 240
=> 20 *Height = 240
=> Height = 12 m


Dimension of room are 4m ×6m ×12 m

Answer 2

Let breadth of the room be b units
Then,Length=(50/100)×b+b=(b/2+b)=3b/2....(i)
Area of the floor=l×b sq.units=(3b/2)×b=3b²/2
Cost of carpeting the room=(3b²/2)×(77/2)
924=231b²/4⇒231b²=924×4⇒b²=(924×4)/231=16⇒b=√16=4m
Length=(3×4)/2=6m.....by using(i)
Area of 4 walls of the room=2(l+b)×h sq.units
=2(6+4)×h=20h
Cost of painting the walls=20h×(11/2)
1320=110h⇒h=1320/110=12m
∴Length=6m,Breadth=4m,Height=12m.