Four men and 6 women can complete a certain piece of work in 5 days whereas three men and 4 women can complete it in 7 days. How many men should assist 25 women to complete $$2\frac{1}{2}$$ times the same work in 5 days?

Total work = number of (man\woman) $$\times time$$

Four men and 6 women can complete a certain piece of work in 5 days whereas three men and 4 women can complete it in 7 days so,

(4m + 6w) $$\times 5 = (3m + 4w) \times 7$$

20m + 30w = 21m + 28w

m = 2w

Now,

Work =  $$2\frac{1}{2}$$ times the same work

Work = $$\frac{5}{2}$$ $$\times$$ same work

(m/w) $$\times 5 = \frac{5}{2} \times (4m + 6w) \times$$ 5

w $$\times 5 = \frac{5}{2} \times (4 \times 2w + 6w) \times$$ 5 

w$$\times 5 = \frac{5}{2} \times 14w \times$$ 5

w = 35 women

So need for worker = 25w + 10 w

Number of man = 10 $$\times$$ m/2 = 5 man