The length, breadth and height of a room are 1, b and h respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls is

examrobotsa's picture

Submitted by examrobotsa on

Q: 141 (IAS/1997)
The length, breadth and height of a room are 1, b and h respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,4,0,4,1,3

keywords: 

{'perimeter': [0, 1, 1, 0], 'ceiling': [0, 1, 0, 3], 'total area': [1, 1, 0, 0], 'walls': [2, 1, 1, 4], 'room': [0, 1, 3, 4], 'percentage': [1, 2, 2, 3], 'length': [0, 0, 1, 0], 'height': [0, 0, 1, 2], 'breadth': [1, 2, 1, 1]}

The perimeter of the ceiling is calculated by surrounding the edges. Since the ceiling is a rectangle, its perimeter is given by twice the sum of length and breadth (2*(1+b)).

The total area of the four walls, excluding the ceiling and floor, is calculated by adding the area of each rectangular wall together. This total area is 2*(1 + b)*h.

The percentage of the ceiling`s perimeter to the total area of the walls is calculated by: Ceiling Perimeter/ Total Wall Area *100. Simplifying this equation becomes: 2*(1 + b)/2*(1 + b)*h*100.

After canceling identical terms, the expression simplifies to 100/h, matching option 2.

Option 1 (100h), 3 (h) and 4 (h/100) are wrong as they do not involve proper unit conversion (either omitting, or wrongly incorporating height h in the equation). Thus, option 2 (100/h) is the correct answer.