Hint: Assume the capacity of each jug to be 300 ml
Given,
In Jug 1:
1/3 is filled with apple juice = 100 ml apple juice
Rest is filled with orange juice = 200 ml orange juice.
In Jug 2:
2/3 is filled with apple juice = 200 ml apple juice
Remaining Capacity in Jug 2 = 300 - 200 ml = 100 ml.
This is filled by the mixture in the first jug which has apple juice: orange juice in a 1:2 ratio.
So, this means that 1/3 of 100 ml = 33 ml will be apple juice & 2/3 of 100 ml = 67 ml will be orange juice
Finally,
The content of juices in Jug 2:
Apple Juice = 200 ml apple juice + 33 ml apple juice = 233 ml of apple juice
Orange Juice = 67 ml orange juice
Fraction of Orange Juice = 67/ 300 = 2/9