Answer it for English language

The information states that the taxable income in the fifth band was Ksh. 25,580. This means his total taxable income extended beyond the fourth band.
The total income up to the end of the fourth band is:

$$24,000 + (32,333 - 24,000) + (41,410 - 32,333) + (50,420 - 41,410)$$ $$= 24,000 + 8,333 + 9,077 + 9,010 = 50,420 \text{ Ksh.}$$

The total taxable income is the sum of income up to the fourth band and the income in the fifth band:

$$\text{Total Taxable Income} = 50,420 + 25,580 = 76,000 \text{ Ksh.}$$

The taxable allowances are the house allowance and the commuter allowance. The danger allowance is not typically taxable unless specified.

$$\text{Taxable Allowances} = \text{House Allowance} + \text{Commuter Allowance}$$ $$\text{Taxable Allowances} = 18,000 + 6,000 = 24,000 \text{ Ksh.}$$

$$\text{Total Taxable Income} = \text{Basic Salary} + \text{Taxable Allowances}$$ $$76,000 = \text{Basic Salary} + 24,000$$ $$\text{Basic Salary} = 76,000 - 24,000$$ $$\text{Basic Salary} = \boxed{\text{Ksh. } 52,000}$$

The total taxable income is Ksh. 76,000.

• Band 1: Ksh. 24,000 at 10% $$\text{Tax} = 0.10 \times 24,000 = 2,400 \text{ Ksh.}$$
• Band 2: (Ksh. 32,333 - 24,000) = Ksh. 8,333 at 15% $$\text{Tax} = 0.15 \times 8,333 = 1,249.95 \text{ Ksh.}$$
• Band 3: (Ksh. 41,410 - 32,333) = Ksh. 9,077 at 20% $$\text{Tax} = 0.20 \times 9,077 = 1,815.40 \text{ Ksh.}$$
• Band 4: (Ksh. 50,420 - 41,410) = Ksh. 9,010 at 25% $$\text{Tax} = 0.25 \times 9,010 = 2,252.50 \text{ Ksh.}$$
• Band 5 (Remaining): (Ksh. 76,000 - 50,420) = Ksh. 25,580 at 30% $$\text{Tax} = 0.30 \times 25,580 = 7,674.00 \text{ Ksh.}$$

$$\text{Total Gross Tax} = 2,400 + 1,249.95 + 1,815.40 + 2,252.50 + 7,674.00$$ $$\text{Total Gross Tax} = 15,391.85 \text{ Ksh.}$$

$$\text{PAYE} = \text{Total Gross Tax} - \text{Personal Relief}$$ $$\text{PAYE} = 15,391.85 - 2,400$$ $$\text{PAYE} = \boxed{\text{Ksh. } 12,991.85}$$