Question

The cost of papering the wall of a room, 12 m long, at the rate of Rs. 6.50 per square meter is Rs. 1638 The cost of matting the floor at Re. 3.50 per square metre is Rs. 378. Find the height of the room

Answer 1

Therefore the height of the room is 6 cm.

Step-by-step explanation:

Let the height of the room be h and breadth of the room be b.

Given that the cost of papering the wall of the room 12 m long at the rate Rs 6.50 per m²

Therefore the surface area of four wall is= $2\times height (length+breadth)$

                                                                  = 2×h(12+b) m²

So, the cost of papering the wall is =Rs. (2×h(12+b)× 6.50)

Again the cost of matting floor at Rs. 3.50 per m²

Then the surface area of the floor is = length × breadth

                                                            = (12×b) m²

The cost of matting the floor is = Rs.(12×b×3.50)

According to the problem,

12×b×3.50= 378

⇒b = 9 cm

Again,

2×h(12+b)× 6.50 =1638

⇒2×h(12+9)× 6.50 =1638    [ since b = 9 cm]

⇒h =$\frac{1638}{2\times 21\times 6.50 }$

⇒ h = 6 cm

Therefore the height of the room is 6 cm.