4 men and 3 women complete a task in 8 days. If 6 men and 8 women work on the same task, they will take half the time. How long will a man and a woman take to complete the task?

Explanation:

Let ‘m’ be the amount of work done by a man in a day. Let ‘w’ be the amount of work done by a woman in a day.

Then, 4 men and 3 women will complete 4m + 3w work in a day = 1\8th of the total task.

Therefore, if 8 men and 6 women work, they will complete twice as much work or 1\4th of the tasx.

i.e., 8m + 6w = 1\4th of the task in a day …eqn (1)

6 men and 8 women will complete 6m + 8w work in a day

= 1\4th of the task in a day …eqn (2)

Adding eqn (1) and eqn (2), we get 14m + 14w = 1\4+1\4 = 1\2 of the task.

Therefore, 1m + 1w will complete 1\14×1\2 = 1\28th of the task in a day.

Or a man and a woman working together will take 28 days to complete the task.