An isolated particle of mass m is moving in a horizontal plane (x-y), along the x-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4 . An instant later, the smaller fragment is at y = + 15 cm. The larger fragment at this instant is at : 

 y = -5 cm

Before explosion, particle was moving along x-axis i.e. it has no y-component of velocity. Thus, the center of mass will not move in y-direction or we can say y_cm = 0.

Now : \(y_{cm} = \frac{m_1\times y_1 + m_2 \times y_2}{m_1 + m_2}\)

\(0 = \frac{\frac{m}{4} \times 15+\frac{3m}{4} \times y}{\frac{m}{4}+\frac{3m}{4}}\)

$\Rightarrow 15m+3my = 0$

\(\Rightarrow y = - 5 \text{ cm}\)