Magnetic Field of Straight Wires question from JEE Main 2024 (4 Apr, Shift 2)

Answer: 5

1. Same-direction currents: at points outside both wires the fields add. Let $k = \frac{\mu_0}{2\pi}$.
2. At A ($r$ from $I$, $3r$ from $2I$): $B_A = k\left(\frac{I}{r} + \frac{2I}{3r}\right) = \frac{5kI}{3r}$
3. At C ($r$ from $2I$, $3r$ from $I$): $B_C = k\left(\frac{2I}{r} + \frac{I}{3r}\right) = \frac{7kI}{3r}$
4. $\frac{B_A}{B_C} = \frac{5}{7}$, so $x = 5$