Final answer:
It will take 4 men and 8 women a total of 24 days to complete the work.
Step-by-step explanation:
To determine how many days it will take for 4 men and 8 women to complete the work, we need to calculate the rates at which each group completes the work. From the given information, we know that 16 men can complete the work in 5 days, which means 1 man's work rate is 1/80 of the total work per day (as 16 men will complete the work in 5 days). Similarly, 20 women can complete the work in 12 days, which means 1 woman's work rate is 1/240 of the total work per day (as 20 women will complete the work in 12 days).
To find out how many days it will take for 4 men and 8 women to complete the work, we can add their individual work rates. Together, 4 men will complete 4/80 = 1/20 of the total work per day, and 8 women will complete 8/240 = 1/30 of the total work per day. Adding these rates together, their combined work rate is 1/20 + 1/30 = 5/120 = 1/24 of the total work per day. Therefore, it will take them 24 days to complete the work.
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