The greatest ratio in each pair:

$13:25;17:10$

$13:25\text{\hspace{0.17em}and\hspace{0.17em}}17:10$

$13:25=\frac{13}{25}\text{\hspace{0.17em}and\hspace{0.17em}}17:10=\frac{17}{10}$

L.C.M. of 25 and 10 $=50$

$=\frac{13}{25}\times 50\text{\hspace{0.17em}and\hspace{0.17em}}\frac{17}{10}\times 50$

$=13\times 2\text{\hspace{0.17em}and\hspace{0.17em}}17\times 5$

$=26\text{\hspace{0.17em}and\hspace{0.17em}}85$

$\therefore 26<85$

$\Rightarrow 13:25<17:10$