A can do a work in 36 days. He worked at it for 4 days and then B finished the remaining work in 24 days. In how many days A and B together finish the work.

1 day work of $A=\frac{1}{36}$

4 days work $B=4\times \frac{1}{36}=\frac{1}{9}$

Remaining work $=1-\frac{1}{9}=\frac{8}{9}$

B completed the remaining work in 24 days

let B alone completes the work in x days

$\frac{1}{x}\times 24=\frac{8}{9}\to x=27 days$

1 day work of A & B $\Rightarrow \frac{1}{36}+\frac{1}{27}\Rightarrow \frac{3+4}{108}\Rightarrow \frac{7}{108}$

Hence A and B together can finish the work in $\Rightarrow \frac{108}{7}\Rightarrow 15\frac{3}{7} Days$