Final answer:
It will take 10 men and 8 women approximately 0.581 days (or about 14 hours) to complete the job.
Step-by-step explanation:
Let's first find the amount of work done by each man in one day. Since 12 men take 18 days to complete the job, that means that each man can complete 1/12th of the job in one day (1 job / 12 men = 1/12 job per man per day).
Similarly, let's find the amount of work done by each woman in one day. We know that 12 women can complete 4/3 part of the job in 18 days. So, each woman can complete 4/3 part of the job / 12 women = 1/9 part of the job in one day (4/3 job / 18 days = 1/9 job per woman per day).
Now, let's calculate the total work done by 10 men and 8 women in one day. 10 men can complete 10*(1/12) = 5/6 part of the job in one day, and 8 women can complete 8*(1/9) = 8/9 part of the job in one day. Therefore, the total work done by them in one day is 5/6 + 8/9 = 15/18 + 16/18 = 31/18 part of the job.
To find out how many days it will take for them to complete the job, we can divide the total work required (1 job) by the work done in one day (31/18 job). So, it will take 1 / (31/18) = 18/31 days.
Therefore, 10 men and 8 women together will take approximately 0.581 days (18/31 days) to complete the same job.