Question

A room is 1.5 times as long as it is
broad. The cost of carpeting the room
at Rs 18 per sq. m is Rs 972 and the
cost of white washing the four walls
at the rate of Rs 6 per sq. m is Rs
1080. Find the dimensions of the
room. (Non-anonymous question o)​

Answer 1

Step-by-step explanation:

Let the breadth of the room be am

⇒ Length of the room=a+

2

a

=

2

3a

m

Area of the rooma×

2

3a

=

2

3a

2

sq.m

⇒ Cost of carpeting the room at Rs.3.25per sq.m=Rs.3.25×

2

3a

2

⇒75.50=3.25×

2

3a

2

⇒a

2

=

3.25×3

175.50×2

=36

⇒a=6

⇒ Breadth=a=6m and length=

2

3×6

=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 walls−Area of 1 door and 2 windows

=(30h−8)sq.m

⇒Cost of papering walls at Rs.1.40per sq.m=Rs.(30h−8)×1.40

⇒240.80=(30h−8)×1.40

⇒30h−8=

1.40

240.80

=172

⇒30h=172+8=180

⇒h=

30

180

=6m

Hence, dimensions of the room are

Length=9m, Breadth=6m and Height=6m