5 men working together can finish a piece of work in 10 days. 10 women can finish the same piece of work in 7.5 days. If 3 men and 3 women work together than how much time will it take to complete the work?

5 men working together can finish the work in 10 days. Let each man does x units of work in 1 day. So total work to be done = 50x
Now 10 women finish the work in 7.5 days. Hence, if y is the amount of work done by 1 women in 1 day then total work = 10*7.5 = 75y
50x = 75y
=> x/y = 3/2
So, let y = 2x/3
When 3 men and 3 women work, then the amount of work done by them in 1 day = 3x + 2x = 5x
Hence it will take 10 days to complete 50 units of work.