Question 40423
Given,
     w+x+y+z = 60 
  => 1/2(x+y+z)+(x+y+z) = 60 ;[As w = 1/2(x+y+z)]
  => 3/2(x+y+z) = 60
  => x+y+z = 40              ;[multiplying both sides by 2/3]
  
Again 
     w+x+y+z = 60
  => w+40 = 60               ;[because x+y+z=40]       
  => w = 20                  ;[subtracting 40 from both sides]

Given 
     w+x+y+z = 60
  => (w+y+z)+1/3(w+y+z) = 60 ;[given x=1/3(w+y+z)]
  => 4/3(w+y+z) = 60
  => w+y+z = 45              ;[multiplying both sides by 3/4]         

Again 
     w+x+y+z = 60
  => x+45 = 60               ;[because w+y+z = 45]
  => x = 15                  ;[subtracting 45 from both sides]

Given 
     w+x+y+z = 60
  => (w+x+z)+1/4(w+x+z) = 60 ;[given y=1/4(w+x+z)]
  => 5/4(w+x+z) = 60
  => w+x+z = 48              ;[multiplying both sides by 4/5]         

Again 
     w+x+y+z = 60
  => y+48 = 60               ;[because w+x+z = 48]
  => y = 12                  ;[subtracting 48 from both sides]

We know,
     w+x+y+z = 60
  => 20+15+12+z = 60         ;[as w=20, x=15, y=12]
  => z = 13

The solution is:
  w=20, x=15, y=12 and z=13