an isolated particle of mass m moving in horizontal plane [x-y]along x-axis at acertain height above the ground it suddenly exploded into fragments of masses m/4& 3m/4 an instant later smaller fragment is at y=15 cm. the larger fragment at this instant is at?

As the particle is exploded only due to its internal energy. So net external force during this process is 0. So the centre mass will not change.
Let the particle while explosion was above the origin of the co-ordinate system. i e just before explosion X=0 and Y=0

Centre of mass will be at X=0 and Y=0

after explosion Centre of mass will be at X=0 and Y=0

Ycm= [(m/4 * 15) + (3m/4 * y)]/m =0

solving y=-5cm

Regards

Arun