Two parallel wires separated by a distance of 10 cm carry currents...

Let the third wire be placed at a distance $x$ from the $10 \text{ A}$ wire.

For the third wire to experience zero magnetic force, the net magnetic field at its position must be zero.

Since the currents in the two wires are in the same direction, the magnetic fields produced by them will be in opposite directions only in the region between the wires.

Equating the magnitudes of the magnetic fields produced by the two wires at distance $x$ from the $10 \text{ A}$ wire:

$B_1 = B_2$

$\dfrac{\mu_0 I_1}{2 \pi x} = \dfrac{\mu_0 I_2}{2 \pi (d - x)}$

Substituting $I_1 = 10 \text{ A}$, $I_2 = 40 \text{ A}$, and $d = 10 \text{ cm}$:

$\dfrac{10}{x} = \dfrac{40}{10 - x}$

$10 - x = 4x$

$5x = 10$

$x = 2 \text{ cm}$

The third wire must be placed $2 \text{ cm}$ from the $10 \text{ A}$ current, between the wires.