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The cost of enclosing a rectangular garden with a fence all around, at the rate of $75$ paise per meter, is $Rs . 300$ . If the length of the garden is $120$ meters, find the area of the field in square meters.

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9600 m^{2}

8400 m^{2}

7500 m^{2}

None of these

answer is A.

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Detailed Solution

Given the cost of fencing of garden at rate of

75

paise per meter is

Rs . 300

. And length of garden is

120 m .

The total cost divided by rate of fencing will give the perimeter of the rectangle.
We know that Rs.1 = 100 paise then,
75paise = Rs.0.75
Thus, the perimeter of the rectangular garden

= \frac{300}{0.75}

\Rightarrow

Perimeter of rectangular garden

= 400

m
Perimeter of a rectangle

= 2 (length + breadth)

\Rightarrow 2 (120 + breadth) = 400

\Rightarrow 120 + breadth = 200

\Rightarrow breadth

=200-120

\Rightarrow breadth = 80

m
Thus, the area of the rectangle

= length \times breadth

\Rightarrow

Area

= 80 \times 120

\Rightarrow

Area

= 9600 m^{2}

So, area of field is

9600 m^{2}

.
Hence, the correct option is 1.

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