3 men and 8 women can complete a work in $$\frac{{75}}{8}$$ days. While 9 men and 12 women can complete it in $$\frac{{25}}{7}$$ days. In how many days will 15 women complete it?

Solution (By Examveda Team)

$$\eqalign{ & \left( {3m + 8w} \right) \times \frac{{75}}{8} = \left( {9m + 12w} \right) \times \frac{{25}}{7} \cr & 63m + 168w = 72m + 96w \cr & 72w = 9m \cr & \frac{m}{w} = \frac{8}{1} \cr & {\text{Total work}} = \left( {3m + 8w} \right) \times \frac{{75}}{8} \cr & = \left( {3 \times 8 + 8 \times 1} \right) \times \frac{{75}}{8} \cr & = 4 \times 75 \cr & {\text{Time taken by }}15w = \frac{{4 \times 75}}{{15 \times 1}} = 20{\text{ day}} \cr} $$