Question

The cost of papering the four walls of a room 12m long at Rs. 6.50 per square meter is Rs. 1638 and the cost of matting the floor at Rs. 3.50 per square meter is Rs. 378. Find the height of the room.
(a) 5 m
(b) 7 m
(c) 6 m
(d) None of these

Answer 1

Hint: In this given problem, we are provided with the cost of papering and matting of floors and walls respectively and also the given length. To start with, we will first try to find the breadth given the papering condition. And once we find it, we will use the matting condition to get our height.

Complete step by step solution:
According to the question, we are given the cost of papering the four walls of a room. Also, the cost of matting the floor is given to us. The length of the wall is also said to be 12 meters.
To start with, we consider that breadth of the room to be, b meters.
Thus, the total area of the floor, we have, $ =l\times b=12\times b $ square meter.
Now, the cost of matting the floor at Rs. 3.50, we get the total cost as, $ =12\times b\times 3.50=42b $
We are also given this cost as Rs. 378.
Hence, we get, 42b = 378
Dividing both sides by 42, we get now, b = 9 meter.
Again, the area of the walls of the room would be, = $ =2\times height\left( 12+9 \right) $ square meter.
Simplifying, we get, $ =2\times 21\times height=42\times height $ square meter.
And we have also the given cost as, Rs. 6.50 per square metre.
Hence, we have the total cost as, $ =6.50\times 42\times height=273\times height $ rupees.
Equaling this with the total cost, we are getting the equation as, $ \Rightarrow 273\times height=1638 $ .
Dividing both sides with 273, we get, the height = 6 m.

So, the correct answer is “Option (c)”.

Note: In this problem, we have dealt with the forms of the dimensions of a room. The area of the room is said to be, $ 2\times height\times \left( length+breadth \right) $ square unit. Again, the area of one floor is said to be, $ length\times breadth $ square units.