The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500.

Circumference $=\frac{\text { Total cost of fencing }}{\text { Rate of fencing }}=\frac{5500}{25}=220$

Let the radius of the circle be r.
​Now,

Circumference $=220$

$\Rightarrow 2 \pi r=220$

$\Rightarrow r=35 \mathrm{~cm}$

Now,

Area of field $=\pi r^{2}=\frac{22}{7} \times(35)^{2}=3850 \mathrm{~cm}^{2}$

Cost of ploughing = Rate ⨯ Area of field = 0.5 ⨯ 3850 = Rs 1925
Hence, the cost of ploughing the field is Rs 1925.