Answer: Easy, I know this one.
Step-by-step explanation:
The city is Chicago.
CHICKEN:it is seven lettered word.so,we will extract the letters out of it as per the given fraction,i.e. 3/7. The letters thus exracted are first 3 letters of the word,which are CHIC.
CAT:this is a three lettered word.So,we will extract first two letters from it(as per the given fraction,that is 2/3).So,the extracted letters are CA.
GOAT:this is a four lettered word.So,we will extract the first two letters out of it(as the given fraction is 2/4).So,the extracted letters are GO.
CHI + CA + GO = Chicago
Hope this helps! :)