6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work 1 day how many men would be required totally?
(Work & Time)

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

$1 m a n ` s 1 d a y w o r k = \frac{1}{6 \times 12} = \frac{1}{72} p a r t ∴ 1 w o m a n 1 d a y w o r k = \frac{1}{8 \times 18} = \frac{1}{144} p a r t ∴ 1 c h i l d 1 d a y w o r k = \frac{1}{18 \times 10} = \frac{1}{180} p a r t n o w, 4 m e n, 12 w o m e n a n d 20 c h i l d r e n c a n d o i n 2 d a y s = 2 (\frac{4}{72} + \frac{12}{144} + \frac{20}{180}) = \frac{8}{72} + \frac{24}{144} + \frac{40}{180} = \frac{1}{9} + \frac{1}{6} + \frac{1}{9} = \frac{9}{18} = \frac{1}{2} p a r t ∴ R e m a i n i n g w o r k = 1 - \frac{1}{2} = \frac{1}{2} p a r t N o w, \frac{1}{72} p a r t o f w o r k i s d o n e i n 1 d a y b y = 1 m a n ∴ \frac{1}{2} p a r t o f w o r k i s d o n e i n 1 d a y b y = \frac{72 \times 1}{2 \times 1} = 36 m e n a n s w e r : 36 m e n .$