What is "بقالك"?

I was going over the dialogue of previous lessons to make sure I had a firm grasp of Arabic grammar, and this stumped me. What exactly does بقالك mean? I understand that the sentence بقالك اد اية بتدرس عربي means "how long have you been studying Arabic", and the lesson mentions that ببقالك translates as "you have been". But in English, "have been" is not a verb in itself, they are just auxiliary words used to indicate the past perfect progressive tense. But I can tell that بقالك is a conjugated verb in itself because of the b- prefix and the -ak suffix. So what is the literal translation of this word then?

i think it means stores or a shop,as i hav heard this word representing to a shop....

This is a very idiomatic use of the verb "yabqa, baqa", which basically means "to stay" or "to remain". "yabqa iSSeef Tawiilan" means 'summer stays for a long time'. But the verb can also convey 'to become', or even 'to be'. Here, we combine the masculine third person past "baqa" , with a preposition+pronoun "lak", 'to you', with the final 'a' lenghthening[phonetic rules], to get "baqaalak" or colloquially "ba'aalak", and it means approximately " it has been to you". "addi ee ba'aalak?" is "quantity what has been to you?", or "how much has become to you". Combine it with a present like "btidrus" and it is "you study, how much it become to you?" or "how long you are studying?" In the Levant, the verb "Saar, biSiir" 'to become' is used exactly the same way.

PPS: the "b" is part of the root. It is not a prefix. If I remember correctly, if you want to add a "b-" colloquial progressive prefix, the verb becomes "byib'a" for 3m present. the above sentence about summer would (ana faakir!) come out "byib'a SSeef mudda Tawilla", which summer has been doing a lot lately "I stay" should then be "bab'a"
Please correct me if I'm wrong, as I'm very rusty !