A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of Aman, a woman and a child are in the ratio $5:4:2$, then a 16 hectare field will be reaped by 6 men, 4 women and 7 children in 

2 men, 3 women and 4 children can reap one hector in one day

Let working capacity ratio is $x$

Hence the total working capaciity is $2\left(5x\right)+3\left(4x\right)+4\left(2x\right)=30x$

$30x=1\Rightarrow x=\frac{1}{30}$

To complete 16 hectors, the man power is $6\left(5x\right)+4\left(4x\right)+7\left(2x\right)=60x$

it implies that $\frac{60}{30}=2$

These people can reap 2 hectors per day

hence total number of days required to complete the task is $\frac{16}{2}=8$