The co-ordinates of centre of mass of particles of mass 10, 20 and 30 gm are (1, 1, 1) cm. The position co-ordinates of mass 40 gm which when added to the system, the position of combined centre of mass be at (0, 0, 0) are,

m₁ = 10, m₂ = 20, m₃ = 30, 

 (x_cm, y_cm, z_cm) = (1, 1, 1)

${\mathrm{x}}_{\mathrm{cm}}=\frac{{\mathrm{m}}_1{\mathrm{x}}_1+{\mathrm{m}}_2{\mathrm{x}}_2+{\mathrm{m}}_3{\mathrm{x}}_3}{{\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3}$

$1=\frac{10{\mathrm{x}}_1+20{\mathrm{x}}_2+30{\mathrm{x}}_3}{60}$

10x₁ +20x₂ + 30x₃ = 60

for 4 particle system m₄ = 40, 

(x¹cm, y¹cm, z¹ cm) = (0, 0, 0,)

${\mathrm{x}\text{'}}_{\mathrm{cm}}=\frac{{\mathrm{m}}_1{\mathrm{x}}_1+{\mathrm{m}}_2{\mathrm{x}}_2+{\mathrm{m}}_3{\mathrm{x}}_3+{\mathrm{m}}_4{\mathrm{x}}_4}{{\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3+{\mathrm{m}}_4}$

$0=\frac{10{\mathrm{x}}_1+20{\mathrm{x}}_2+30{\mathrm{x}}_3+40{\mathrm{x}}_4}{100}$
$\Rightarrow$10x₁ + 20x₂ + 30x₃ + 40x₄ = 0

$\Rightarrow$60 + 40x₄ = 0

$40{\mathrm{x}}_4=-60\Rightarrow {\mathrm{x}}_4=\frac{-60}{40}=\frac{-3}{2}$

similarly ${\mathrm{y}}_4=\frac{-3}{2}, {\mathrm{z}}_4=\frac{-3}{2}$

$\left(\frac{-3}{2}, \frac{-3}{2}, \frac{-3}{2}\right)$