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Question :

2.5 m wide path is running around a square ground, and path's cost of paving is Rs. 8 per m2 and the perimeter of a rectangle plot is 164 m. If difference between the length and breadth of the rectangle is 22 m and the square ground area is 39 m2 less than the area of the rectangle, then what is total cost of paving the path around the square ground?

1. Rs. 3340

2. Rs. 3320

3. Rs. 3360

4. Rs. 3350

5. Rs. 3380

Correct Answer : 2
Solution :

The perimeter of a rectangle = 164 m

2(l + b) = 164

l + b = 82 --- (1)

l - b = 22 ---(2)

By solving the equation (1) and (2), we get,

l = 52, b = 30

Area of rectangle = lb = 52 * 30 = 1560

Area of Square = 1560 - 39 = 1521

Side (a) = 39 m

Outer Side of the path = 39 + 2 * 2.5 = 44 m

So, area of the path = 442 - 392 = (44 - 39)(44 + 39) = 415 m2

Hence, total cost of paving the path = 415 * 8 = Rs. 3320

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