control account

1. If sales were 150,000 and debtors fell by 5,500 then a total of 155,500 must have been received. 96,000 of this was paid into the bank, which leaves 59,500 in cash. Of this, 50,000 was used to pay expenses, which leave 9,500 that should have increased the cash balance. This means that the cash balance should be 9500 + 750 = 10,250.
Since there is no cash left, the bookkeeper must have stolen 10,250.

2. Have you typed out this second question in full?
I ask, because as it stands the answer is 712,500 (the amount owed to the company).
The irrecoverable debt recovered is not relevant because since it had been written off it was not included in receivables. Payments to a debt collector are not relevant – they are an expense and do not affect receivables.
(Incidentally, this must be an old question because the terminology is out-of-date – debtors are now called receivables and bad debts are now called irrecoverable debts. The terminology changed several years ago.)

If the question were to have said that 712,500 was the net balance on receivables, then it would be a different answer. It would mean that 712,500 was the net of the amount owed to the company and the 27,700 owed by the company. In that case 712500 + 27700 = 740200 would be shown as receivables and 27700 would be shown as payables.

You are welcome 🙂