20a = 20/1.21 + 20/2.22+ ... + 20/80.100
= 1-1/21 + 1/2 - 1/22 +...+ 1/80 - 1/100
= 1 + 1/2 + 1/3 +... + 1/19 + 1/20 - 1/81 - 1/82 -.... - 1/100
80b = 80/1.81 + 80/2.82 + 80/3.83 +... + 80/20.100
= 1 - 1/81+ 1/2 - 1/83 +...+ 1/20 - 1/100
=> 20a = 80b
=> a/b = 4