What will be the cost of fencing wire required to border the playground with dimensions $50m\times 5m$ at $₹5/m$?

The given playground is given to us with dimensions: $50m\times 5m$.

We need to find the length of fencing wire which will be required for the ground, which will be equal to the perimeter.

Now, we know that the perimeter of the rectangle is found by the following expression:

$P=2\times (length + breadth)$

Now, substituting the dimensions of the ground, we get:

$P=2\times (50+5) m$

Simplifying this, we get:

$P=110 m$

Thus, the boundary of the park is $110m$ long.

Now for finding the cost of fencing wire, $R$:

$R=₹5\times 110$

Simplifying this,. we get:

$R=₹550$

Hence, the cost of fencing wire required will be option (B) $₹550$.