Question

A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall

leaving all around a margin of 75 cm from the walls. Find the area of the carpet and the area of

the strip left uncovered. If the width of the carpet is 82 cm, find the cost at the rate of Rs 18 per

metre.

Answer 1

Answer:

Solution:-

Length = 22 m and Breadth = 15.5 m

The area of the hall = L × B = 22 × 15.5 = 341 m²

Margin of carpet = 75 cm = 0.75 m

Area of carpet = (22 - 2 × 0.75) (15.5 - 2 × 0.75)

⇒ (22 - 1.5) (15.5 - 1.5)

Area of the carpet = 20.5 × 14 = 287 m²

Portion uncovered = 341 - 287 = 54 m²

A meter length of the carpet = 1 m × 0.82 m = 0.82 m²

287/0.82 = 350 m of carpet

Cost of fencing the strip = Rs.60 per meter

Cost of fencing the strip = 350 × 60

= Rs. 21000

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Answer 2

Solution:

Area of the hall = Length × Width
                          = 22 × 15.5
= 341 m²

Converting into metre,

75cm = 75/100 m = 0.75m

Since the margin is on both the sides we will subtract it twice,

Area of the carpet:

= Length × Width
= (22 - 0.75 - 0.75) × (15.5 - 0.75 - 0.75)
= 20.5 × 14
= 287 m²

Uncovered Area = Total Area - Area of the carpet
                           = 340 - 287 = 53m²

Total Carpet required = 287 m²

Total Cost of carpet = 287 × 60 = Rs 17220.

Hence,

The area of the carpet is 287 m².

The area of the strip left uncovered is 53 m².

The cost of carpet is Rs 17220.