Work done by X in 8 days = \(\left(\frac{1}{40}\times8\right)=\frac{1}{5}\)

Remaining work = \(\left(1-\frac{1}{5}\right)=\frac{4}{5}\)

Now,   \(\frac{4}{5}\)  work is done by Y in 16 days.

Whole work will be done by Y in \(\left(16\times\frac{5}{4}\right)= 20 days.\)

So, X's 1 day's work =  \(\frac{1}{40}\) , Y's 1 day's work = \(\frac{1}{20}\)  

(X + Y)'s 1 day's work = \(\left(\frac{1}{40}+\frac{1}{20}\right) = \frac{3}{40}\)

Hence, X and Y will together complete the work in \(\left(\frac{40}{3}\right) = 13\frac{1}{3}days.\)