A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{10 men}} \times {\text{12 days}} = {\text{10 women}} \times {\text{6 days}} \cr & {\text{2 men}} = {\text{1 woman}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{1}{2}{\text{ }} \cr & {\text{1 man work}} = {\text{1 unit/day}} \cr & {\text{1 woman work}} = {\text{2 unit/day}} \cr & {\text{Total work}} = {\text{10 men}} \times {\text{12 days}} \cr & = 10 \times 1 \times 12 \cr & = 120{\text{ units}} \cr & {\text{Time required}}\left( {{\text{10 men}} + {\text{10 women}}} \right) \cr & = \frac{{{\text{Total work}}}}{{{\text{Efficiency}}}} \cr & = \frac{{120}}{{10 \times 1 + 10 \times 2}} \cr & = \frac{{120}}{{30}} \cr & = 4{\text{ days}} \cr} $$