Question

A door frame of dimensions \[2m \times 1.5m\] is fixed on the wall of dimensions \[12m \times 8m\] .Find the cost of painting the front of the wall if the rate of painting \[1{m^2}\] of the wall is Rs.20.

Answer 1

Hint: Here the door is to be fixed in the wall. So obviously when we will paint the wall we will not paint the door. And this is our answer! In order to find the cost of painting the wall, remove the area of the door from the area of the wall. The remaining area is to be painted.

Complete step-by-step answer:
Given that the dimensions of the wall are \[12m \times 8m\]
So the area of the wall will be a product of its dimensions. So area of the wall is given by,
Area of the wall \[ = 12m \times 8m = 96{m^2}\]
Now the area of the door that is to be fixed in the wall.
Area of the door frame \[ = 2m \times 1.5m = 3{m^2}\]
Since we have found both the areas we will now find the area of the region that is to be painted.
Area of region that is to be painted = Area of the wall - Area of the door frame
Putting the values
\[ \Rightarrow 96{m^2} - 3{m^2} = 93{m^2}\]
This is the area of the wall to be painted. Now it is given that the rate of painting is Rs.20 for \[1{m^2}\]. So the expenditure for this much area to be painted is
Cost of painting \[ \Rightarrow 93{m^2} \times 20 = Rs.1860\]
Thus the cost of painting the wall with the door frame is Rs.1860.

Note: In this problem we removed the area of the door frame because that region is empty and will not be painted. Also note that the rate given is of Rs.20 for \[1{m^2}\] so we multiplied the area with rate.