6 men can complete a piece of work in 12 days, 8 women can complete the same piece of work in 18 days and 18 children can do it in 10 days. 4 men, 12 women and 20 children do the work for 2 days. If the remaining work be completed by men only in 1 day, how many men will be required ?

Solution(By Examveda Team)

6 men will complete the work in 12 days
1 men will complete the work in (6 × 12) = 72 days
8 women will complete two work in 18 days
1 women will complete the work in (8 × 18) = 144 days
18 children will complete the work in 10 days
1 children will complete the work in (18 × 10) = 180 days
$$\eqalign{ & {\text{1 men's 1 day's work}} = \frac{1}{{72}} \cr & {\text{1 women's 1 day's work}} = \frac{1}{{144}} \cr & {\text{1 children's 1 day's work}} = \frac{1}{{180}} \cr} $$
(4 men + 12 women + 20 children)'s 2 day's work
$$\eqalign{ & = 2\left( {\frac{4}{{72}} + \frac{{12}}{{144}} + \frac{{20}}{{180}}} \right) \cr & = 2\left( {\frac{1}{{18}} + \frac{1}{{12}} + \frac{1}{9}} \right) \cr & {\text{L}}{\text{.C}}{\text{.M of 18, 12 and 9}} = {\text{36}} \cr & {\text{ = }}\frac{{2\left( {2 + 3 + 4} \right)}}{{36}} \cr & = \frac{1}{2} \cr & \therefore {\text{Remaining work}} = \frac{1}{2} \cr & \therefore {\text{Required number of men}} \cr & = 72 \times \frac{1}{2} \cr & = 36 \cr} $$