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

Example Input: Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the ? 
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 1 , d ) 8 : 2 , e ) 8 : 4
Example Output: b

Example Input: Problem: what number has a 3 : 4 ratio to the number 400 ? 
Options: a ) 130 , b ) 100 , c ) 200 , d ) 300 , e ) 120
Example Output: d

Example Input: 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 220 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 ) 44 , b ) 64 , c ) 70 , d ) 80 , e ) 84
Example Output:
a