Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B$$_1$$, at its centre when a current I passes through it. The ratio B$$_1$$ : B$$_2$$ is:

The magnetic field at the center of a circular loop is defined as $$B = \frac{\mu_0 n I}{2a}$$

Number of turns ($$n$$) = 3

Radius ($$R$$) = $$a/3$$ (since the same wire length $$L = 2\pi a$$ now forms 3 loops, $$L = 3 \times 2\pi R \implies R = a/3$$)

Current per turn = $$I/3$$

$$B_2 = \frac{\mu_0 \cdot 3 \cdot (I/3)}{2 \cdot (a/3)}$$

$$B_2 = \frac{\mu_0 \cdot I}{2 \cdot (a/3)} = \frac{3\mu_0 I}{2a}$$

$$\frac{B_1}{B_2} = \frac{\mu_0 I / 2a}{3\mu_0 I / 2a} = \frac{1}{3}$$