Calculate Leonard's monthly basic salary in Ksh.

Gross Tax is the tax before deducting personal relief.

• Band 1: $10\%$ of Ksh. 9,680

  $$0.10 \times 9,680 = \text{Ksh. } 968$$

  Remaining Gross Tax = $6,674 - 968 = \text{Ksh. } 5,706$

• Band 2: $15\%$ of (Ksh. $18,800 - 9,680$) = $15\%$ of Ksh. 9,120

  $$0.15 \times 9,120 = \text{Ksh. } 1,368$$

  Remaining Gross Tax = $5,706 - 1,368 = \text{Ksh. } 4,338$

• Band 3: $20\%$ of (Ksh. $27,920 - 18,800$) = $20\%$ of Ksh. 9,120

  $$0.20 \times 9,120 = \text{Ksh. } 1,824$$

  Remaining Gross Tax = $4,338 - 1,824 = \text{Ksh. } 2,514$

• Band 4: $25\%$ of (Ksh. $37,040 - 27,920$) = $25\%$ of Ksh. 9,120

  $$0.25 \times 9,120 = \text{Ksh. } 2,280$$

  Remaining Gross Tax = $2,514 - 2,280 = \text{Ksh. } 234$

• Band 5: The remaining tax of Ksh. 234 falls into the $30\%$ band. Let $x$ be the amount of taxable income in this band.

  $$0.30 \times x = 234$$ $$x = \frac{234}{0.30} = \text{Ksh. } 780$$

The monthly basic salary is $\boxed{\text{Ksh. } 22,600}$.

Net salary is the total taxable income (gross salary) minus total deductions.

His monthly net salary is $\boxed{\text{Ksh. } 24,288}$.