A long wire carrying a steady current is bent into a circular loop of one turn.  The magnetic field at the centre of the loop is B.  It is then bent into a circular coil of n turns.  The magnetic field at the centre of this coil of n turns will be 

In this problem, length of the wire making the coil remains constant. So  where r is the radius of the coil and n is the number of turns.
We know magnetic field produced by a coil of radius ‘r’ and no.of turns n is
$\mathrm{B}=\frac{{\mu }_0\mathrm{ni}}{2\mathrm{r}}$
If $\ell =2\pi rn,\text{ then }r=\frac{\ell }{2\pi n}$
$B\propto n^2$
Here, ${\mathrm{n}}_1=\mathrm{l},{\mathrm{B}}_1=\mathrm{B};\frac{{\mathrm{B}}_1}{{\mathrm{B}}_2}=\frac{1}{{\mathrm{n}}^2}$
$B_2=n^{2}B.$