5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{5M}} \times {\text{6 days}} = {\text{10W}} \times {\text{5 days}} \cr & {\text{3M}} = {\text{5W}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{5}{3} \cr & 1{\text{M}}\left( {{\text{work}}} \right) = 5{\text{ units/day}} \cr & {\text{1W}}\left( {{\text{work}}} \right) = 3{\text{ units/day}} \cr & {\text{Hence, }} \cr & {\text{Total work}} \cr & = \left( {{\text{5M}} \times {\text{6}}} \right) \cr & = {\text{5}} \times {\text{5}} \times {\text{6}} \cr & = {\text{150 units}} \cr & {\text{Required time for }}\left( {{\text{5W}} + {\text{3M}}} \right) \cr & = \frac{{{\text{Total work}}}}{{{\text{Work done/day}}}} \cr & = \frac{{150}}{{\left( {5 \times 3 + 3 \times 5} \right)}} \cr & = \frac{{150}}{{30}} \cr & = 5{\text{ days}} \cr} $$