for example the purchase day book is undercast (understating) by $10,000 where we should correct this amount on payables ledger control account or on ledger account? and why?
The total of the day book is used for posting to the control account in the nominal ledger and so the control account needs correcting.
The total is not used in the payables ledger and so that does not need correcting.
This is all explained in my free lectures on Books of Prime Entry. The lectures are a complete free course for Paper FA and cover everything needed to be able to pass the exam well.