If the time taken by 4 men to complete a piece of work is double the time taken by 5 children to complete the same work. Each man is two times faster than a woman. Then find the time taken by 12 men, 10 children and 8 women to complete the work, given that a child would finish the work in 20 days?

Child completes work in 20 days, so child's rate = 1/20. 4 men take double time of 5 children, so 4 men = 40 days, thus 1 man = 160 days. Each man is 2× faster than woman, so 1 woman = 320 days. Combined rate of 12 men + 10 children + 8 women = 12/160 + 10/20 + 8/320 = 3/40 + 1/2 + 1/40 = 1/2 + 1/10 = 5/10 + 1/10 = 6/10 = 3/5. Time = 1 ÷ 3/5 = 5/3 = 1.67 days ≈ 1 day.