Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?

Let m be the work done by one man in one day, and w be the work done by one woman in one day. From the first condition: 4m + 3w = 1/6 (since they complete 1 job in 6 days). From the second: 5m + 6w = 1/4. Solving these equations: Multiply first by 5: 20m + 15w = 5/6. Multiply second by 4: 20m + 24w = 1. Subtracting: 9w = 1/6, so w = 1/54. Therefore, one woman alone takes 54 days.