1. Abc company books show a cash balance at the commercial bank on October 31, 2021, of birr 20,502.
2. The bank statement for October shows a balance of birr 22,190.
3. A deposit of birr 3,680 does not appear on the bank statement.
4. A cheque written in October but charged in the bank statement:

- Cheque Number 7347: birr 150
- Cheque Number 7348: birr 4,820
- Cheque Number 7349: birr 31

5. Abc has not recorded the interest of birr 600 collected by the bank.
6. Bank service charges of birr 18 are not yet recorded by Abc.
7. The bank returned one of Abc's customer cheques of birr 220.
8. Abc discovered an incorrectly recorded cheque #7382 written in October for birr 131 in payment of an account payable as birr 311.
9. A cheque for Abc company amounting to birr 175 was incorrectly charged to [tex]$Abc$[/tex] accompanied.

### Step-by-Step Solution

#### 1. Initial Balances
The first step is to establish the initial balances as mentioned:
- Cash book balance: 20,502 birr
- Bank statement balance: 22,190 birr

#### 2. Deposits Not Appeared on Bank Statement
There's a deposit of 3,680 birr that has not appeared on the bank statement. This implies the bank statement does not show the actual balance that should include this deposit.

#### 3. Cheques Written and Not Yet Cleared
The cheques written that have not yet been cleared by the bank are:
- Cheque \#7347: 150 birr
- Cheque \#7348: 4,820 birr
- Cheque \#7349: 31 birr

The total amount of these cheques is:
[tex]\[ 150 + 4820 + 31 = 5001 \text{ birr} \][/tex]

#### 4. Adjustments for the Cash Book Balance

- Interest Collected by Bank: +600 birr
- Bank Service Charges: -18 birr
- Returned Cheque: -220 birr
- Incorrect Recording of Cheque \#7382: It should be 131 birr, but was recorded as 311 birr. Therefore, you need to correct this by adding back the difference:
[tex]\[ 311 - 131 = 180 \text{ birr} \][/tex]

Combining these adjustments:
[tex]\[ 20,502 + 600 - 18 - 220 + 180 = 21,044 \text{ birr} \][/tex]

So, the adjusted cash book balance is 21,044 birr.

#### 5. Adjustments for the Bank Statement Balance

- Deposit Not Appeared: +3,680 birr
- Cheques Written: -5,001 birr
- Bank Error: An incorrect amount of 175 birr was charged to the company’s account and should be added back.

Combining these adjustments:
[tex]\[ 22,190 + 3680 - 5001 + 175 = 20,694 \text{ birr} \][/tex]

So, the adjusted bank statement balance is 20,694 birr.

### Final Adjusted Balances
- Cheque Total: 5,001 birr
- Adjusted Cash Book Balance: 21,044 birr
- Adjusted Bank Statement Balance: 20,694 birr

These adjustments correct the discrepancies and align the cash book balance and bank statement balance for reconciliation purposes.