Some things to notice: Some one has informed him about the panic state his folks are in. When akaash decides to call the police, immediately they get to know it is Arnav who is calling them. He is not in Scotland ( the catch here is scotland-he has or he is doing some detective service)--- he may have installed some cameras, and getting to know the pulse of every member.
Third point-- Arnav has feigned his confession to Khushi just to read her pulse and test her innocence.
Another possible twist- Arnav may have staged his kidnap, and shyam may come to know of this.. In the meantime, Khushi may frantically want talk to arnav about the papers.. this is when she may overhear Shyam mentioning Arnav's name. She may not confront Shyam directly about the kidnap.. but may follow him and that's how she will help arnav escape from the kidnappers, and arnav would also know of her innocense.
Khushi will in her true sense, get help arnav escape from his kidnappers ( this is a fake kidnap; and will join together to nab Shyam)..
The another twist that CVs are speaking of and rumours floating the India forums is that-- khushi may realise that arnav has downplayed with her first for not trusting her, second for playing with her innocence and feelings.. she may leave the RM house, this will coincide with nk' s re- entry.