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

[Q]: Problem: two integers are in the ratio of 1 to 3 . if 10 is added to the smaller number , the ratio becomes 2 to 1 . find the larger integer . 
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
[A]: a


[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: find the ratio between whole surfaces of a sphere and a hemisphere ? 
Options: ['a ) 4 : 3', 'b ) 3 : 4', 'c ) 3 : 2', 'd ) 5 : 2', 'e ) 4 : 6']
[A]:
a