divide 243 into 3 parts such that half of the first part , one -third of the second part and one-fourth of the third part are all equal.

Let The Parts Be x,y And z.

Now

x+y+z = 243

And

Accordingly To The Question

x/2 = y/3 = z/4

Or

3x = 2y

y = 3x/2

x/2 = z/4

2z = 4x

z = 4x/2 = 2x

Now 

x+3x/2+2x = 243

9x/2 = 243

x = 243*2/9 = 54

So x = 54

z = 2x = 108

y = 3x/2

y = 81

So Parts Are 54,81 And 108.