Let the mass of each part be $\large\frac{m}{5},\frac{m}{5},\frac{3m}{5}$

Momentum of each part flying at right angle will be same and at $45^{\circ}$ with the third part.

$\large\frac{m}{5}$$ \times 15 \cos 45 +\large\frac{m}{5}$$ \times 15 \cos 45=\large\frac{3m}{5}$$v$

$\large\frac{15}{\sqrt 2}+\frac{15}{\sqrt 2}$$=3v$

$v= \large\frac{10}{\sqrt 2}$

$\quad=5 \sqrt 2\;m/s$

Hence b is the correct answer.