The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. How long will 12 men, 10 children and 8 women take to complete a job, given that a child would finish the job in 20 days ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{By using formula}} \cr & {{\text{M}}_1}{{\text{D}}_1}{{\text{H}}_1} = {{\text{M}}_2}{{\text{D}}_2}{{\text{H}}_2} \cr & {\text{According to the question,}} \cr & {\text{5C}} = {\text{4M}} \times {\text{2}} \cr & \frac{{\text{M}}}{{\text{C}}} = \frac{5}{8}\left( {{\text{Efficiency ratio}}} \right) \cr & {\text{Again,}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{2}{1}\left( {{\text{Efficiency ratio}}} \right) \cr & \,\,\,\,{\text{M }}:{\text{ W }}:{\text{ C}} \cr & \,\,\,\,{{\text{2}}_{ \times 5}}:{\text{ }}{1_{ \times 5}} \cr & \,\,\,\,{5_{ \times 2}}:\,\,\,\,\,\,\,\,\,\,\,\,\,\,{8_2} \cr & \overline {{\text{ }}10{\text{ }}:{\text{ }}5{\text{ }}:{\text{ }}16{\text{ }}} \cr & {\text{Now, }} \cr & {\text{20C}} = \left( {{\text{12M}} + {\text{10C}} + {\text{8W}}} \right) \times {\text{D}} \cr} $$
$$20 \times 16 = $$   $$\left( {12 \times 10 + 10 \times 16 + 8 \times 5} \right)$$     $$ \times {\text{D}}$$
$$\eqalign{ & 320 = 320{\text{D}} \cr & {\text{D}} = \frac{{320}}{{320}} = 1 \cr & \boxed{{\text{D}} = 1{\text{ day}}} \cr} $$