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

Example Input: Problem: a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ? 
Options: a ) 6000 , b ) 9000 , c ) 9500 , d ) 12000 , e ) none
Example Output: b

Example Input: Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30
Example Output: d

Example Input: Problem: in a certain neighborhood , there are half as many beige houses as white houses , and 6 times as many white houses as brown houses . what is the ratio of the number of brown houses to the number of beige houses ? 
Options: a ) 1 : 3 , b ) 1 : 9 , c ) 2 : 5 , d ) 5 : 3 , e ) 6 : 1
Example Output:
a