If 52 men can do a piece of work in 27 days, how long will 39 men take to complete the same work 

Taking  $x_1=52,x_2=39,y_1=27,y_2=y$

By the problem  $x_1{y}_1=x_2{y}_2$

$52\times 27=39\times y_2$

$y_2=\frac{52\times 27}{39}=36days$

39 men will be the work in 36 days.