Reasons why the trial balance may balance even with mistakes i n the books of accounts?

Trial Balance consists of the balances of the ledger accounts. The mistakes, if any, are at the journalizing level, but as long as the principles of double entry, where every credit has an equal debit, is followed, the Trial Balance are bound to tally. 

Because trial balance only shows closing balances of accounts for a particular date. If there is a mistake in posting, then it affect the accounts related to the voucher but as per double entry system, both debit & credit are posted in the books so trial balance will always b balanced.

Trial balance is a prima facie evidence that debit and credit balances have been posted correctly. This means there can be an error but if it's repeated on the other side too, then the trial balance would still tally but that wouldn't mean that all balances from chart of accounts have been posted correctly. 

trial balance shows closing balance of each ledgers of chart of account on a particular date. if posting mistake is there so that can be effected on related ledger of chart of account by voucher, and the double entry system there are debit & credit posted in books off accounts so that trail always will be balanced.

A trial balance is supposed to be balanced when both debit side and credit side are equal.

But equal debits and credits do not guarantee the accuracy of the debited or credited amount.

For example, you paid for a computer. You were supposed to make the following double entry:

Dr. Asset

Cr. Cash/Bank

However, you erroneously made the following double entry:

Dr. Receivable

Cr. Cash/Bank

Although this double entry would balance the trial balance, yet it remains conceptually an incorrect entry.

A trial balance might fail to balance for a variety of reasons. For example, if you transposed numbers while posting from the general journal to the general ledger, or from the ledger to the trial balance sheet, this could cause the trial balance to not equal out. Also, if you made a math error, this can cause a problem too. Or perhaps you credited something that should have been debited or vice versa, or you applied a transaction to the wrong account. If you bought $500 worth of office supplies with your credit card but accidentally posted it as a cash transaction, this will throw off your trial balance.

equal mistakes 

equal mistakes 

equal mistakes 

Trail Balance is showing All the chart of accounts General ledger closing balance even you pass the journal entery with wrong amount, the debit & credit account will be the equal and this double entry will effect in the accounts general ledger closing balance. 

TB is a result of a number of the transaction but it does not mention the accuracy of the recorded transaction.

There are many cause to trial Balance may Balance even mistakes. 1. If same Amount Debit and same Amount Credit Entry wrongly. If Ledger entry and Journal Entry Wrong. If Transaction no Entry and So On.

per double entry system, both debit & credit are posted in the books so trial balance will be balanced