Question

The cost of papering the walls of the room 12m long at the rate of Rs 1.35 per sq.m is Rs 340.20 and cost of carpeting the floor at Rs 0.85per sq. m is Rs 90.80. Find the height of the room.

Answer 1

Given:
Length of room( l) = 12 m
Let the breadth of room = b m
height of room = h m
Cost of carpeting the floor @ ₹ 0.85 per m² =₹ 90.80.
floor area = cost /area = 90.80 / 0.85 = 106.8 m²
⇒ l × b = 106.8
⇒ 12 × b = 106.8
⇒ b = 106.8/12
⇒ b = 8.9 m
cost of papering wall @ ₹ 1.35 per m² =₹ 340.20
Area of four walls = lateral surface area = 340.20 / 1.35 = 252 m²
2h(l+b) = 252
2h(12+8.9) = 252
2h×20.9 = 252
h = 252/(2×20.9) = 252/ 41.8
h = 6.02 m ≈ 6 m
Hence, the Height of the room is 6m.

Answer 2

According to question

Length of Room   L = 12 m

Total area of room except the Floor = 2 (B*H + L*H) + L * H
  

thus Total cost of papering   = 340.20 Rs
     1.35 * 2[ ( BH + 12H) ] + 12 H = 340.20
           [ 2 (BH + 12 H) +  12 H ] =   252
              2 BH +  24 H + 12 H = 252
                2 BH + 36 H = 252
                      BH + 18 H = 126
                        H ( B + 18 ) = 126

Also      0.85 *  LB = 90.80
                 0.85 *  12 * B  = 90.80
                                  B = 8.90
thus                         H = 126 /  26.90
                                 H = 4.68 m