The cost of papering the four walls of a room 12 m long at ₹ 6.50 per square metre is ₹ 1,638 and the cost of matting the floor at ₹ 3.50 per square metre is ₹ 378. Find the height of the room.

Given,

Length = 12 m

Cost of papering (4 walls) = ₹ 1,638 at ₹ 6.50 per m².

Cost of matting (Floor) = ₹ 378 at ₹ 3.50 per m².

Calculating the floor area,

Floor area = $\dfrac{\text{Total cost of matting}}{\text{Rate}}$

= $\dfrac{378}{3.50}$

= 108 m².

Calculating width of the room,

Floor area = l × b

⇒ 108 = 12 × b

⇒ b = $\dfrac{108}{12}$ = 9 m

Calculating the area of four walls,

Area of four walls = $\dfrac{\text{Total cost of papering}}{\text{Rate}}$

= $\dfrac{1638}{6.5}$

= 252 m².

Calculating the height of the room,

Area of four walls = [2(l + b)h]

⇒ 252 = [2(12 + 9) × h]

⇒ 252 = 2(21) × h

⇒ 252 = 42 × h

⇒ h = $\dfrac{252}{42}$

⇒ h = 6 m.

Hence, height of the room = 6 m.