Explanation:

Let's assume 3 parts of amount are x,y andz.

x+y+z=2379

SI for x= x*5*2/100=> x/10

Total amount after 2 years - x+(x/10)= 11x/10 ------------(1)

SI for y= y*5*3/100=> 15y/100

Total amount after 3 years - y+(15y/100) = 115y/100 -------(2)

SI for z= z*5*4/100=> z/5

Total amount after 4 years - z+(z/5) = 6z/5 ---------------(3)

As per the conditions "3 parts amounts after 2, 3 and 4 years respectively may be equal" (1) = (2) = (3)

based on the above condition and x+y+z=2379, we can get x= 828, y= 792 and z= 759