A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per sq.m is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.

• A. b=5; l=6; H=18
• B. l=5; b=18; H=18
• C. l=6; b=18; H=15
• D. b=6; l=18; H=6

Answer: (D)

Let breadth = x metres, length = 3x metres, height = H metres.  Area of the floor=(Total cost of carpeting)/(Rate) = (270/5) sq.m = 54 sq.m  x × 3 x 2 = 54 ? x 2 = 54 × 2 ? x = 6    So, breadth = 6 m and length = 3 6 2  = 9 m. Now, papered area = (1720/10) =  172 sq.m  Area of 1 door and 2 windows = 8 sq.m  Total area of 4 walls = (172 + 8) sq.m = 180 sq.m  2 × 9 + 6 H = 180 ? H = 6