In what ratio should a 6.5 N ${\mathrm{HNO}}_3$ be diluted with water to get 3.5 N ${\mathrm{HNO}}_3$?

Using cross wise rule 

$x=3.5-0=3.5$

$y=6.5-3.5=3.0$

The dilution ratio is 3.5 : 3 or 7 : 6, i.e., 6 volumes of water should be added to 7 volumes of 6.5 N solution to get 3.5 N ${\mathrm{HNO}}_3$ solution.