Shortcut method to find slip in induction motor
The slip is the fractional difference between synchronous and actual speed.

You have done exactly the minimum number of calculations required to get that from the information given. Starting from this information, there is no shorter cut.

It might be slightly quicker if you precompute the synchronous frequencies before the exams and remember them, so in a 50Hz system, 2 and 4 pole motors have synch speeds of 3k and 1.5krpm, and they're 3.6k and 1.8k in 60Hz land. But that won't work with questions that ask you about other frequencies!

It will be yet quicker if you precompute the difference for 1% slip for all the different frequencies and pole numbers. So with 50Hz/4 pole with 1500 synch frequency, 1% is 15rpm. Then in the exam, 1470rpm is obviously 30rpm short, so it's 2%. But that won't work with questions that ask you to show your working!

Given that you know how to calculate it, and can, I would not suggest you burden your memory with precomputed single-purpose equations, but instead practice on speeding up your general arithmetic skills.