4 men and 8 women can complete a certain piece of work in 8 days where as 6 men and 8 women can complete it in 6 days. How many men should assist 24 women to complete \(\frac{5}{2}\) times the same work in 8 days?

9

Total work = Efficiency × Time

(4M + 8W) × 8 = (6M + 8W) × 6 

32 M + 64 W = 36 M + 48 W

16 W = 4 M

4 W = 1 M

Efficiency :-    M : W = 4 : 1

Total work = (4 M + 8 W) × 8 = ( 16 + 8 ) × 8 = 192

Now,

Let total required efficiency to do the work = \(x\)

\(x\) × 8 = 192 × \(\frac{5}{2}\)

\(x\)  = \(\frac{480}{8}\)

\(x\) = 60

We have 24 women + n no. of men

Efficiency of 24 women = 24

Required efficiency = 60 - 24 = 36

Efficiency of 1 man = 4

therefore, for 36 efficiency total men required = \(\frac{36}{4}\) = 9