Let's assume that there are X kilograms of bananas in the first basket and Y kilograms of bananas in the second basket, and establish the equation according to the meaning of the question:

x- 10=y+ 10

(3/ 10)(x- 10)=( 1/3)(y- 10)+5

Solving equation: x=60

y=40

Answer: there are 60 kilograms of bananas in basket A and 40 kilograms in basket B.