X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

Solution (By Examveda Team)

Work done by X in 8 days = $$ {\frac{1}{{40}} \times 8} $$   = $$\frac{1}{5}$$
Remaining work = $$ {1 - \frac{1}{5}} $$   = $$\frac{4}{5}$$
Now, $$\frac{4}{5}$$ work is done by Y in 16 days
Whole work will be done by Y in = $$ {16 \times \frac{5}{4}} $$   = 20 days
∴ 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
$$\eqalign{ & = {\frac{1}{{40}} + \frac{1}{{20}}} \cr & = \frac{3}{{40}} \cr} $$
Hence, X and Y will together complete the work in
$$\eqalign{ & = {\frac{{{\text{40}}}}{{\text{3}}}} \cr & {\text{ = 13}}\frac{{\text{1}}}{{\text{3}}}\,\,{\text{days}} \cr} $$