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

[Q]: Problem: in a ratio which is equal to 7 : 9 , if the antecedent is 42 , then the consequent is ? 
Options: a ) 72 , b ) 54 , c ) 64 , d ) 51 , e ) 45
[A]: b


[Q]: Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 6000 . their h . c . f is ? 
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 100
[A]: e


[Q]: Problem: the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ? 
Options: a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90
[A]:
a