A alone can do a work in 24 days. Time taken by A in completing 1/3 of work is equal to the time taken by B in completing 1/2 of the work. In what time A and B together will complete the work.

Time taken by A in completing 1/3 of work

$= 24 imes frac{1}{3} = 8$ days

8 day = time taken by B in completing 1/2 of work

B alone will complete the work = 16 days

Required time

$= frac{{16 imes 24}}{{left( {24 + 16} ight)}} = 9frac{3}{5}$ days