Question regarding lesson 1.4

Should the first "ka" in the following sentence not be a "ke"?
एक कमरे का एक रात का किराया कितना है?
Reason (in my thinking): the second "ka" (preceding किराया) should trigger the oblique case.

एक कमरे का एक रात का किराया कितना है? is correct.

 

Great, thank. Could also explain why? I am comparing it with the expression
आज के राकेट हि'दी के पाठ मे  where the "का" becomes "के" because "पाठ" is in oblique.

Why is this not the case here?