12 men or 18 women can do a job in 14 days. In how many days work will be finished by 8 men and 16 women

Sure, let's solve this step by step:

Step 1: First, we need to find the work done by one man and one woman in one day. According to the problem, 12 men can complete the job in 14 days. So, the work done by one man in one day would be 1/(1214). Similarly, 18 women can complete the job in 14 days, so the work done by one woman in one day would be 1/(1814).

Step 2: Now, we need to find the combined work done by 8 men and 16 women in one day. This would be 8/(1214) + 16/(1814).

Step 3: To find out how many days they will take to complete the job, we take the reciprocal of the value obtained in step 2. This will give us the number of days required to complete the job.

Let's calculate:

Work done by 1 man in 1 day = 1/(1214) = 0.00595 Work done by 1 woman in 1 day = 1/(1814) = 0.00397

Work done by 8 men and 16 women in 1 day = 80.00595 + 160.00397 = 0.0476 + 0.06352 = 0.11112

So, the number of days required to complete the job = 1/0.11112 = 8.99 days

Therefore, the work will be finished by 8 men and 16 women in approximately 9 days.