Two cars P,Q are travelling towards each other from two different points A and B respectively. Car P breaks down after travelling for half an hour. Q meets P 2 hrs after they started. Had the car P not broken-down, Q would have met P 1 h 20 mins after starting. What is the ratio of the speed of the cars?

P=X Q=Y Y/X=5/4

Q/P is 5/4
Let P travel p km/hr and Q travel q km/hr. In 30 mins P would have travelled p/2 kms and since Q meets P 2 hours after travelling it would have covered 2q kms. Total Distance= p/2+ 2q.
Next it says if P never broke down, so they both start from opposite directions and at the same time, u will use the concept of relative speed. Formula- Total distance /( speed of P + Speed of Q)- we add the denominator as they are coming from opp direction, if it was same direction then we subtract.
Using the formula-
(p/2+2q)/ (p+q)= 4/3 ( solving 1 hour 20 mins gives 4/3 in fraction form). On solving this equation you get Q/P=5/4 or P/Q=4/5. Hope this helps.

8/7
or 7/8