A 10 hectare field is reaped by 2 men,3 women, and 4 children in 10 days .If a man , a women and a child work in the ratio 5:4:2 ,a 16 hectare field will be reaped by 6 men,4 women and 7 children ni how many days?

• 8 days
  
  Given ratio of work of a man, woman & a child = 5 : 4 : 2
  Expressing work of women and children in terms of man for calculation of total work.
  According to ratio m/w=5/4 => w=(4/5)m and m/c=5/2 => c=(2/5)m
  So total work of 2 men, 3 women and 4 children = 2m + 3*(4/5)m + 4*(2/5)m = 6m and
  Total work of 6 men, 4 women and 7 children = 6m + 4*(4/5)m + 7*(2/5)m = 12m
  According to men, days and work relationship, M1*D1/W1 = M2*D2/W2
  Here M1=6m, D1=10 days, W1=10 (hectare) and M2=12m, W2=16 (hectare), we have to find D2= ?
  Therefore 6m*10/10 = 12m*D2/16
  => D2=8
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