Let

A=12 x

B = 15 x

C = 25 x

Given that Sum of A, B and C = 312

12 x + 15 x + 25 x = 312

32 x = 312

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$(C) 3 :10 .$