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?

18 days

(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