Suppose the bowls contain s spoons of water (w) and tea (t). After the first transfer, the tea bowl contents are
st+w
After the second transfer, the water bowl contains
(s-1)w + (s*t+ w)/(s+1)
= (s/(s+1))(s*w+ t)
After the second transfer, the tea bowl contains
(s/(s+1))(s*t+ w)
The proportion of each liquid in the other bowl is the same.
st+w
After the second transfer, the water bowl contains
(s-1)w + (s*t+ w)/(s+1)
= (s/(s+1))(s*w+ t)
After the second transfer, the tea bowl contains
(s/(s+1))(s*t+ w)
The proportion of each liquid in the other bowl is the same.