The cost of painting the walls of a cuboidal room at the rate of Rs. 25 per m2 is Rs. 8800. If the ratio of length and height of room is 3 : 2 and breadth is of 10m, then find the sum of the cost of painting the ceiling of the room assuming that it also being painted at Rs.25 per m2 and the cost of paving the floor where the cost of paving is Rs. 75 per m2

The cost of painting the walls of a cuboidal room at the rate of Rs. 25 per m2 is Rs. 8800. If the ratio of length and height of room is 3 : 2 and breadth is of 10m, then find the sum of the cost of painting the ceiling of the room assuming that it also being painted at Rs.25 per m2 and the cost of paving the floor where the cost of paving is Rs. 75 per m2 Correct Answer Rs. 12000

Given:

The cost of painting the walls of a cuboidal room at the rate of Rs. 25 per m² is Rs. 8800

The ratio of length and height of room is 3 : 2 and breadth is of 10m

The cost of paving is Rs. 75 per m²

Formula used:

Area of four walls of cuboid = 2 (l + b) × h

Area of ceiling = Area of floor = l × b

Calculation:

Let the ratio be x

So, length = 3x

And height = 2x

So, area of four walls = 2 (3x + 10) × 2x = (12x² + 40x)     ----(i)

Since, cost of painting the walls of room is Rs. 8800 at the rate of Rs. 25 per m²

So, area of four walls = 8800/25 = 352 m²      ----(ii)

From (i) and (ii)

12x² + 40x = 352

⇒ 3x² + 10x - 88 = 0

⇒ 3x² + 22x – 12x – 88 = 0

⇒ x (3x + 22) – 4 (3x + 22) = 0

⇒ (3x + 22) (x – 4) = 0

So, x = 4 or x = -22/3 (it is not possible)

So, length = 3 × 4 = 12 m

And height = 2 × 4 = 8 m

(area of cieling = l × b = 12 × 10 = 120 m² = area of the floor)

So, the total cost = (25 × 120 + 75 × 120)

Hence, Rs. 12000