Question

two resistors of 10 ohm and 15 ohm resistance are connected in series what is the ratio of the potential difference across the ends

Answer 1

If two resistors are connected in a series current through them will be same.
So
$v = ir$
in above formula, I is same for both the resistors.

so
$v1 = ir1 \\ v2 = ir2$
taking a ration of above two equations I will be cancelled
so
$\frac{v1}{v2} = \frac{r1}{r2}$
that is your answer