Length of a room is twice its height and its breadth is $1\dfrac{1}{2}$ times its height. The cost of white washing the walls at the rate of ₹ 32 per sq. m is ₹ 3,584. Find the cost of tiling the floor of the room at ₹ 135 per sq. m.

Let h be the height of the room.

Length = 2h

Breadth = $1\dfrac{1}{2}$ h = $\dfrac{3}{2}$ h

The total surface area of 4 walls of the room = 2 x (length + breadth) x height

= 2 x (2h + $\dfrac{3}{2}$ h) x h

= 2 x $\big(\dfrac{4 + 3}{2}\big)$ h x h

= 2 x $\dfrac{7}{2}$ h x h

= 7 h²

Cost of whitewashing walls = ₹ 32 per sq. m

Total cost of whitewashing = ₹ 3,584

⇒ Rate x surface area = total cost

⇒ 32 x 7h² = 3584

⇒ 224 h² = 3584

⇒ h² = $\dfrac{3584}{224}$

⇒ h² = 16

⇒ h = $\sqrt{16}$

⇒ h = 4 m

Length = 2h = 4 x 2 m = 8 m

Breadth = $\dfrac{3}{2}$ h = $\dfrac{3}{2}$ x 4m = 6 m

Floor area = l x b

= 8 x 6

= 48 m²

Cost of tiling = ₹ 135 per sq. m

Total cost of tiling = 48 x ₹ 135

= ₹ 6480

Hence, the cost of tiling the floor = ₹ 6480.