JEE Main 2021 — Magnetic Effects of Current Question with Solution

A long solenoid with $1000 \mathrm{turns} {\mathrm{m}}^{-1}$ has a core material with relative permeability $500$ and volume ${10}^3{ \mathrm{cm}}^3.$ If the core material is replaced by another material having relative permeability of $750$ with same volume maintaining same current of $0.75 \mathrm{A}$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right).$ Find the value of $x.$