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

[Q]: Problem: the hcf of two numbers is 23 and the other two factors of their lcm are 13 and 14 . what is the largest number ? 
Options: a ) 280 , b ) 284 , c ) 292 , d ) 320 , e ) 322
[A]: e


[Q]: Problem: in what ratio should a 20 % methyl alcohol solution be mixed with a 50 % methyl alcohol solution so that the resultant solution has 40 % methyl alcohol in it ? 
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 2 : 3 , d ) 2 : 1 , e ) 3 : 1
[A]: b


[Q]: Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 6 . what is the ratio of the smaller number to the larger number ? 
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3
[A]:
c