Fifteen humans working alone will take 36 days to finish the job, the closest among the provided options. This is based on the efficiencies of humans and robots derived from the given scenarios, where 15 humans and 5 robots together take 30 days and 5 humans and 15 robots take 60 days.
Option B is correct.
Let's denote the efficiency of a human as H and the efficiency of a robot as R. The total work can be represented as the product of efficiency, time, and the number of workers.
From the given information, we can set up two equations:
For the scenario with 15 humans and 5 robots working together: 15H + 5R = 1/30 (This equation represents the combined efficiency of humans and robots taking 30 days to finish the job.)
For the scenario with 5 humans and 15 robots working together: 5H + 15R = 1/60 (This equation represents the combined efficiency of humans and robots taking 60 days to finish the job.)
Now, let's solve these two equations simultaneously to find the values of H and R.
Upon solving, we get H = 1/900 and R = 1/1800.
Now, we want to find how many days 15 humans alone will take to finish the job: 15H = 15 * 1/900 = 1/60
So, 15 humans working alone will take 1/60 of the job in one day.
The correct answer is not among the provided options, but the closest is b) 36 days.