12. 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 m² is Rs. 1420. If a door and 2 windows occupy 8 sq. m, find the height of the room.

A.	4 m	B.	4.5 m
C.	5 m	D.	5.5 m

Answer & Explanation

Answer: Option C

Explanation:
Let breadth = x m, length = 3x m, height = H metres.
Area of the floor = (Total cost of carpeting)/(Rate/m²)=(270/5)m²=54m².
x× (3x/2) = 54 =>x² = (54×2/3) = 36 x = 6.
So, breadth = 6 m and length =(3/2)×6 = 9 m.
Now, papered area = (1420/10)m² = 142 m².
Area of 1 door and 2 windows = 8 m².
Total area of 4 walls = (142 + 8) m² = 150 m²
2×(9+ 6)× H = 150 H = 150/30 = 5 m.

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