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First let us suppose that the depth of the pit is x .

We know that the shape of the pit is in cuboids shape

Hence the volume of the cuboids is length $ \times $ breadth $ \times $ depth .

It is given that the length $ \times $ breadth = $50cm \times 50cm$ and depth of the pit is equal to x .

hence the volume of pit is equal $50cm \times 50cm \times xcm$

that is equal to $2500x$ $c{m^3}$

So the volume of the pit is $2500x$ $c{m^3}$

Now we have to calculate the volume of the pit from some other method as it is given in the question that the one stroke of spade removes $500$ $c{m^3}$ .

And it is also given that $250$ strokes of spade is required for the removal of the earth .

Hence total volume removed by pit is equal to No of stokes $ \times $ Volume removed in one stokes

that is equal to $500 \times 250c{m^3}$

Now we have to equate both the volumes i.e volume of pit and volume removed through pit

Volume of Pit = Total volume of removed through pit

$2500x = 500 \times 250$

Hence $x = \dfrac{500 \times 250}{2500}$

$x = \dfrac{500}{10}$

$x = 50$ cm

Hence the depth of the pit is $x = 50$ cm

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