A field is in the form of a circle. A fence is to be erected around the field.

We know that the circumference C of a circle of radius r is

$C=2 \pi r$

It is given that cost of fencing around the circular field would be Rs.2640 at the rate of Rs.12 per meter. So,

$2 \pi r \times 12=2650$

$24 \times \frac{22}{7} r=2650$

$r=\frac{2650 \times 7}{24 \times 22}$

$=35 \mathrm{~m}$

We know that the area A of circle of radius r,

$A=\pi r^{2}$

Substituting the value of r

$A=\frac{22}{7} \times 35 \times 35$

$=3850 \mathrm{~m}^{2}$

Since, cost to plough per $\mathrm{m}^{2}$ field $=$ Rs. $0.50$

Then, cost to plough $3850 \mathrm{~m}^{2}$ field $=$ Rs. $0.50 \times 3850$

$=$ Rs. 1925

Hence, amount required to plough the field is Rs. 1925 .