A banquet hall is long and broad. A carpet is laid inside the hall leaving around a margin of from the walls. If the width of the carpet is , its cost at the rate of Rs. 20 per meter is Rs. ____.

Question

A banquet hall is  long and  broad. A carpet is laid inside the hall leaving around a margin of  from the walls. If the width of the carpet is , its cost at the rate of Rs. 20 per meter is Rs. ____.

Accepted Answer

Concept- A banquet hall is

long and

broad. A carpet is laid inside the hall leaving around a margin of

from the walls.
Here, we will first determine the size of the banquet hall before determining the length and width of the carpet that will cover the floor and, consequently, its size. The amount left uncovered will be calculated by deducting the carpet's covered area from the hall's overall area.
We will now calculate the required number of carpet strip

and their associated cost.
It is given that a banquet hall is

long and

broad.
Now that we are aware, we can calculate the area of a rectangle by using the formulas:

As a result, the banquet area is provided by:
area of banquet

area of banquet

Given that the carpet is now spread inside the hallway with around a

from the walls.
Now we know that,

Hence,

As a result, the carpet's length should be as follows:

Similar to that, the carpet's recommended breadth is:

Now, the carpet's coverage area is determined by:
area of carpet to cover

area of carpet to cover

Now, we must deduct the carpeted area from the overall area of the hall in order to get the amount that is left uncovered.
As a result, the area exposed is given by:
area covered

area covered

The length of the carpet is a given

Moreover, consider the carpet's width

The quantity of strips needed to cover the area that is

broad is given by:-
number of strips

number of strips

Hence, 16.67 strips of carpet of

length is required to cover the hall with

from each side uncovered.
As a result, the total distance covered is given by:
length

length

Considering that 1 meter costs 20 Rs.
As a result, the price of 400.8 meters is:

Hence, the price is Rs.