If  5 men or 3 boys can do a piece of work in 10 days, the number of days required to complete the work by 6 men and 2 boys is

$5m\left(or\right)3boys\Rightarrow 5m=3b\Rightarrow m=\frac{3}{5}b\to \left(1\right)$

$\Rightarrow b=\frac{5}{3}m$

$\therefore 6m+2b=x$

$6m+2\times \frac{5}{3}m=x$

$6m+\frac{10}{3}m=x\Rightarrow 18m+10m=3x\Rightarrow 28m=3x$

$m=\frac{3x}{28}$

$5m=10\Rightarrow \frac{28m}{3}=x$

$M_1{D}_1=M_2{D}_2$

$50=\frac{28}{3}x\Rightarrow x=\frac{150}{28}=\frac{75}{14}$

$x=5\frac{5}{14}days$