Question

A door-frame of dimensions 3m $\times $ 2m is fixed on the wall of dimension 10m $\times $ 10m. Find the total labour charges for painting the wall if the labour charges for painting $1{{\text{m}}^{2}}$of the wall is Rs.2.50

Answer 1

Hint: To solve this question, first find the area of the wall which is to be painted and the area of the door-frame and subtract the area of the door frame from the area of the wall. As the wall and the door-frame are in the shape of a rectangle, use the formula, area of rectangle = length $\times $ breadth to find the area.

Complete step-by-step answer:
We have the dimensions of the wall and the dimensions of the door-frame. Let us first find out the area of the wall which needs to be painted.

Area of the wall = length of the wall $\times $ breadth of the wall
                             = 10 $\times $ 10
                             =$100{{\text{m}}^{2}}$
Now, here we have the area of the wall as 100 sq. meters.
Further, now let us calculate the area of the door-frame which occupies 3m $\times $ 2m of the space on the wall.
Area of the door frame = length of the door-frame $\times $ breadth of the door-frame
                                          = $3\times 2$
                                          = $6{{\text{m}}^{2}}$
Here, we have the area of the door frame as 6 sq. meters.
Now to find the area which needs to be painted, subtract the area of the door-frame from the area of the wall.
Area which needs to be painted = Area of the wall – Area of the door-frame
                                                          = 100 – 6
                                                          = 94
Therefore, we found out that the area which needs to be painted is $94{{\text{m}}^{2}}$.
Now, the next step is to find the total labour charges required for painting the wall. Here, we have the labour charges for painting $1{{\text{m}}^{2}}$ is Rs. 2.50.
Therefore, let us find the labour charges to paint $94{{\text{m}}^{2}}$. Let us consider the total labour charges for painting the wall as ‘$x$’.
1 = 2.50
94 = $x$
$x$ = $94\times 2.50$
     = 235
Hence, the total labour charges for painting the wall is Rs. 235.

Note: Here, in this question if you notice the dimensions of the wall, it has 10m $\times $ 10m which states that both the measurements are the same. So, the wall is in square shape, although either formula, area of rectangle = $\text{l }\times \text{ b}$ or area of square = ${{s}^{2}}$can be used to find its value.