An arithmetic error in the total of a book of prime entry results in an incorrect figure being posted to the ledger. This creates a discrepancy between the total debits and total credits, thereby preventing the Trial Balance from balancing.

A trial balance checks the equality of total debits and total credits. If an amount is entered twice as a debit without a corresponding credit entry, the trial balance will fail to balance. Errors like complete omission or incorrect classification (capital vs. revenue) do not affect the equality of the trial balance totals, as they maintain the double-entry balance, albeit with incorrect figures or accounts.

The cashbook was debited correctly with $123. However, X's account was debited with $132 instead of being credited with $123. This creates a total error of $123 (the missing credit) + $132 (the incorrect debit) = $255. This discrepancy causes the trial balance to be out of balance by $255.

A partial omission occurs when one side of a transaction is recorded but the corresponding entry is missed. This creates an inequality between total debits and credits, directly causing the trial balance to fail to balance. Other errors, like complete omissions or errors of principle, often maintain the equality of debits and credits.

Nominal accounts represent revenues and expenses, which directly determine net profit. Errors in these accounts impact the income statement directly. While errors in real or personal accounts might affect the balance sheet, the statement provided focuses on the direct impact on profit calculation, which is inherently tied to nominal account balances.