Question

A banquet hall is 25m long and 17m broad. A carpet is laid inside the hall leaving around a margin of 50cm from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is 96cm, then find its cost at the rate of Rs20 per meter.

Answer 1

Hint: Here first we will find the area of the banquet hall and then we will find the length and breadth of the carpet to cover the floor and hence its area. Then we will find the area uncovered by subtracting the area covered by the carpet from the total area of the hall. Now we will find the number od=f strips of carpet required and hence their cost.

Complete step-by-step answer:
It is given that a banquet hall is 25m long and 17m broad.
Now we know that the area of a rectangle length l width b is given by:-
\[area = l \times b\]
Hence the area of banquet is given by:-
\[{\text{area of banquet}} = 25 \times 17\]
Solving it we get:-
\[{\text{area of banquet}} = 425{m^2}\]
Now it is given that carpet is laid inside the hall leaving around a margin of 50cm from the walls.
Now we know that, \[1cm = \dfrac{1}{{100}}m\]
Hence, \[50cm = 0.5m\]
Therefore, the length of the carpet to cover is:-
\[l = 25 - 0.5 - 0.5\]
\[ \Rightarrow l = 24m\]
Similarly the breadth of the carpet to cover is:-
\[b = 17 - 0.5 - 0.5\]
\[b = 16m\]
Now the area of the carpet to cover is given by:-
\[{\text{area of carpet to cover}} = 24 \times 16\]
Solving it we get:-
\[{\text{area of carpet to cover}} = 384{m^2}\]
Now in order to find the area uncovered we have to subtract the area covered by the carpet from the total area of the hall.
Hence the area uncovered is given by:-
\[{\text{area covered}} = 425 - 384\]
\[ \Rightarrow {\text{area covered}} = 41{m^2}\]
It is given that the width of the carpet \[ = 96cm\]
Also, the breadth of the carpet \[ = 16m\] \[ = 1600cm\]
Now, number of strips required to cover the area which is 16m broad is given by:-
\[{\text{number of strips}} = \dfrac{{1600}}{{96}}\]
\[ \Rightarrow {\text{number of strips}} = 16.67\]
Hence 16.67 strips of carpet of 24m length is required to cover the hall with 50cm from each side uncovered.
Hence, the total length covered is given by:-
\[length = 16.67 \times 24\]
\[ \Rightarrow length = 400.8m\]
Now since the cost of 1 meter is 20 Rs.
Therefore, cost of 400.8 meters is:-
\[{\text{cost}} = 400.8 \times 20\]
\[ \Rightarrow {\text{cost}} = 8016Rs\]

Therefore, the cost is 8016 Rs.

Note: Students might forget to find the total length we need to cover by multiplying 16.67 by 24 and then find the total cost which will lead to the wrong solution.
Students should note that in order to find the length and breadth covered by the carpet we need to subtract 0.5m from each side of the floor.