Let
$A=12 x$
$B = 15 x$
$C = 25 x$
Given that the Sum of A, B, and C = 312
$\implies 12 x + 15 x + 25 x = 312$
$\implies 32 x = 312$
$\implies x = 6$
Now,
$A = 12 x = 72$
$B= 15 x = 90$
$C = 25 x = 150$
Difference between B and A = 90- 72 = 18
Difference between C and B = 150 - 90 = 60
$\frac{Difference \ between\ B \ and \ A}{Difference \ between \ C \ and \ B }$ = $\frac{18}{60}=\frac{3}{10}$
Hence,Option $(C) 3 :10 .$