Final answer:
Writing off a $500 bad debt reduces both the accounts receivable and allowance for doubtful debts by $500, leaving the net recoverable amount unchanged. Therefore, the correct answer to the question is b. The recoverable amount would remain the same.
Step-by-step explanation:
When a bad debt of $500 is written off, the balance in the 'allowance for doubtful debts' account is reduced by the amount of the written-off bad debt. The accounts receivable balance is also reduced by the $500 written off. The 'recoverable amount' in the statement of financial position reflects the net value of the accounts receivable after deducting the allowance for doubtful debts.
As both the accounts receivable and allowance for doubtful debts are reduced by the same amount ($500), the net effect on the recoverable amount is zero. Therefore, the correct answer to the question is b. The recoverable amount would remain the same.