The distance between Delhi and Agra is $233$ km. A car $P$ started travelling from Delhi to Agra and another car $Q$ started from Agra to Delhi along the same road $1$ hour after the car $P$ started. The two cars crossed each other $75$ minutes after the car $Q$ started. Both cars were travelling at constant speed. The speed of car $P$ was $10$ km/hr more than the speed of car $Q$. How many kilometers the car $Q$ had travelled when the cars crossed each other?