Question

please give a very clear explanation dont use any shortcut

Answer 1

let A do work in x days and B do work in y days .

we know,
both work together in (xy)/(x + y) days

hence,
xy/(x + y) = 8 days


now both start work together and after 6 days A left the work .

both do work within 6 days ,

hence,
both do 6/8 part of work in 6days .
rest (1-6/8) part of work doing by only B

hence, 1/4 part of work do by B in 6 days
hence, complete work do by B in 6 x 4 =24 days.

but B do complete work in y days .
so, y = 24 days

24x/(24+x) = 8

3x. = 24 + x

x = 12 days