If $$\frac{(x - y)}{5} = \frac{(y - z)}{3} = \frac{(z - x)}{2}$$, then which of these is TRUE?

 $$\frac{(x-y)}{5}=\frac{(y-z)}{3}=\frac{(z-x)}{2}$$

$$3(x-y)=5(y-z).$$

or, $$3x-3y=5y-5z$$

or, $$8y=3x+5z..............\left(1\right)$$

Again, 

$$\frac{y-z}{3}=\frac{z-x}{2}$$

or, $$2y-2z=3z-3x$$

or, $$2y+3x=5z.$$ Put this value in (1) 

$$8y=2y+3x+3x.$$

or, $$6y=6x.$$

or, $$y=x.$$

So, we can say that ,

$$\frac{x-x}{5}=\frac{z-x}{2}\ \left(Given\ equation\right)$$

or, $$\frac{z-x}{2}=0.$$

or, $$x=z.$$

so, $$x=y=z.$$

B is correct choice.