The centre hall of a school is 18m long and 12.5m wide. A carpet is to be laid on the floor leaving a strip 50 cm wide near the walls, uncovered. Then the area of the carpet and uncovered portion.

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195.5

m 2

and 29.5

m 2

183.5

m 2

and 26.5

m 2

205.5

m 2

and 18.5

m 2

None of these

answer is A.

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Detailed Solution

It is given that the length of the central hall is 18m and the breadth of the central hall is 12.5m.
Width of the strip to leave on the side of floor is 50cm = 0.5m
Now we have to calculate the length and breadth of the carpet to find its area
So the length of the carpet = length of the floor – 2 × width of the strip
Length of the carpet =18 − (2 × 0.5) = 18 – 1 = 17m
Now, breadth of the carpet = breadth of the floor – 2 × width of the strip
Breadth of the carpet =12.5 − (2 × 0.5) = 12.5 – 1 = 11.5m
Now, breadth of the carpet = breadth of the floor – 2 × width of the strip
Breadth of the carpet = 12.5 − (2 × 0.5) = 12.5 − 1 = 11.5m
Therefore, area of the carpet = length of the floor × breadth of the floor
Area of the carpet =17×11.5=195.5