Two containers contain equal quantities of milk and water respectively. Half the contents of the first are poured in the second and then the same is transferred back into the first container. This is done three times. What is the ratios of milk to water in the two containers at the end of the process?

1) 5:2, 2:5
2) 5:4, 4:5
3) 14:13, 13:14
4) 11:13, 13:11
5) none of these

• MILK container --- WATER container
  
  (quantity | concentration=milk/total) --- (quantity | concentration=milk/total)
  
  
  1L | 1 --- 1L | 1
  1/2L | 1 --- 3/2L | (1*1/2)/(3/2)=1/3
  1L | 1/2*1+1/3*1/2=2/3 --- 1L | 1/3
  
  1/2L | 2/3 --- 3/2L | (2/3*1/2 + 1/3*1)/(3/2)=4/9
  1L | 2/3*1/2+4/9*1/2=5/9 --- 1L | 4/9
  
  1/2L | 5/9 --- 3/2L | (5/9*1/2 + 4/9)/(3/2)=13/27
  1L | 5/9*1/2+13/27*1/2=14/27 --- 1L | 13/27
  
  
  Therefore, at the end of 3rd iteration in the first container, Milk/Water = 14/(27-14)=14/13 and in the other it is 13/14.
• 5 years agoHelpfull: Yes(1) No(4)