A body of mass M at rest explodes into three pieces, in the ratio...

Let the masses of the three parts be $m ' , m '$ and $2m '$.

Momentum of first part ${p}_{1} = m ' \times 30 = 30m '$ and momentum of second part ${p}_{2} = m ' \times 40 = 40m '$.

Third part will fly in a direction opposite to the direction of resultant of ${p}_{1}$ and ${p}_{2}$, so that total momentum of the system after explosion remains zero.

Momentum of the third part is ${p}_{3} = \sqrt{{p}_{1}^{2} + {p}_{2}^{2}} = \sqrt{{\left(30m '\right)}^{2} + {\left(40m '\right)}^{2}} = 50m '$

Velocity of third part, $v = \dfrac{50m '}{2m '} =$$25m{s}^{- 1}$