The cost of painting the walls of a cubical room is Rs.8640 at the rate of 15 Rs. /m². Find the cost of painting four walls of a cuboidal room having length and breadth 2 m more and 2 m less than side of cube respectively and height is equal to side of cube. (Note: Rate of painting is same in both the cases)

The correct option is Rs.8640.

Step 1: Understand the cost and rate of painting the cubical room.
The total cost of painting the walls of a cubical room is Rs. 8640.
The rate of painting is Rs. 15 per m².
The walls of a room refer to its lateral surface area (4 walls).

Step 2: Find the lateral surface area of the cubical room.
Area of 4 walls of the cubical room = Total Cost / Rate

$\text{Area of 4 walls}=\frac{8640}{15}=576{\text{m}}^2$

Step 3: Find the side length of the cubical room.
Let $a$ be the side of the cube.
The lateral surface area of a cube (area of 4 walls) is given by:

$4a^2=576$

$a^2=\frac{576}{4}=144$

$a=\sqrt{144}=12\text{m}$

Step 4: Determine the dimensions of the cuboidal room.
Length ($l$) = Side of cube + 2 m = 12 + 2 = 14 m
Breadth ($b$) = Side of cube - 2 m = 12 - 2 = 10 m
Height ($h$) = Side of cube = 12 m

Step 5: Calculate the area of 4 walls of the cuboidal room.
The formula for the area of 4 walls of a cuboid is $2h(l+b)$.

$\text{Area}=2\times 12\times (14+10)$

$\text{Area}=24\times 24=576{\text{m}}^2$

Step 6: Calculate the cost of painting the 4 walls of the cuboidal room.
Since the rate of painting remains the same (Rs. 15 per m²):

$\text{Cost}=576\times 15=\text{Rs.}8640$

Thus, the cost of painting the four walls of the cuboidal room is Rs.8640.