In this task, you need to provide the correct option for a given problem from the provided options.

Q: Problem: two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ? 
Options: a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109

A: c
****
Q: Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 19 ! 
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16

A: a
****
Q: Problem: a firm is comprised of partners and associates in a ratio of 2 : 63 . if 35 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ? 
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20

A:
b
****