X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

S and T can do a piece of work in 40 days and 24 days respectively. S started the work alone and then after 5 days T joined him till the completion of the work. How long did the work last?

$A$ can do a piece of work in $25$ days, which $B$ alone can do in $20$ days. A started the work and was joined by $B$ after $10$ days. The work lasted for
(a) $12\frac{1}{2}$ days
(b) $15$ days
(c) $16\frac{2}{3}$ days
(d) $14$ days