6 men and 10 women can complete a given work in 18 days. If 5 more women joined them then they could finish \(\frac{2}{3}\)rd of the work in 10 days. Find the time taken by 30 children to finish the same work. If it is given that women are 20% more efficient than children?
Answer & explanation
Correct answer: option 1
(6 M + 10 W) × 18 = (6 M + 15 W) × 10 × \(\frac{3}{2}\)
108 M + 180 W = 90 M + 225 W
18 M = 45 W
\(\frac{M}{W}\) = \(\frac{5}{2}\) ----- (i)
M : W : C
6 : 5 (20%)
5 × 3 : 2 × 3 (from eqn (i))
15 : 6 : 5
Total work = (6 × 15 + 10 × 6) × 18 = 2700 Unit
30 children would do it in = \(\frac{2700}{30 × 5}\) = 18 days