Four masses $150,250,200$ and $300$ kg are rotating in the same plane at radii of $0\mathrm{.}25,0\mathrm{.}2,0\mathrm{.}3$ and $0\mathrm{.}35$ m $,$ respectively. Their angular location is $40,120$ and $250$ from mass $150$ kg $,$ respectively, measured in counterclockwise direction.

Find the position and magnitude of the balance mass required, if its radius of rotation is $0\mathrm{.}25$ m $,$ by using

i$)$ Numerical method

ii$)$ Graphical method