Question

A can do a piece of work in 12 days whereas B can destroy the work in 3 days. A does the work for 10 days and then B destroys the work up to 2 days. In how many days will the work be finished?

Answer 1

Fraction of work accomplished W at the end of day t will be denoted W(t).
W(0)=0
W(10)=5/6
W(12)=5/6-2/3=1/6
W(22)=1/6+5/6=1 work completed.