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?
Answer & explanation
Correct answer: option 3
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