The internal length of a room is two times its breadth and three times its height. The total cost of painting its four walls at the rate of ₹25/m$$^2$$ is ₹3,600. What is the cost of laying a carpet on its floor at the rate of ₹90.50/m$$^2$$?

let the height of room = $$ x$$

According to question length = $$2x$$ and breadth = $$3\dfrac{3}{2}$$

Area of walls = $$\dfrac{3600}{25} =144 m^2 $$

then $$2(l +b)h =144 $$

$$\Rightarrow2 (3x +\dfrac{3x}{2}) \times x = 144$$

$$\Rightarrow 2 (\dfrac{6x +3x}{2}) x =144 $$

$$\Rightarrow 2 \dfrac{9x}{2}x = 144$$

$$\Rightarrow x^2 =\dfrac {144}{9} =16 $$

$$\Rightarrow x =4 $$

cost of laying carpet = $$ l \times b \times 90.5 $$

$$\Rightarrow 3 \times 4 \times \dfrac {3}{2} \times4 \times 90.5 $$

 $$\Rightarrow 72 \times 90.5$$

$$\Rightarrow 6516 $$ Ans