One, (20 points) According to the "Personal Income Tax Law of the People's Republic of China," citizens do not need to pay tax on their monthly wages and salaries up to 800 yuan, and the portion exceeding 800 yuan is the taxable income for the whole month. In October 2005, the Standing Committee of the National People's Congress passed a revision: starting from January 1, 2006, citizens do not need to pay tax on their monthly wages and salaries up to 1600 yuan, and the portion exceeding 1600 yuan is the taxable income for the whole month. This tax is calculated progressively according to Table 1:
Table 1
\begin{tabular}{|c|c|}
\hline Monthly taxable income & Tax rate \\
\hline Up to 500 yuan & $5 \%$ \\
\hline Over 500 yuan to 2000 yuan & $10 \%$ \\
\hline Over 2000 yuan to 5000 yuan & $15 \%$ \\
\hline$\ldots \cdots$ & $\cdots$ \\
\hline
\end{tabular}
In January 2006, Mr. Zhang paid 54 yuan less in tax on his monthly wages and salaries compared to the same amount of wages and salaries in the past. Mr. Liu and Mr. Wang both paid 80 yuan less in tax. The monthly wages and salaries of the three gentlemen did not exceed 3000 yuan.
(1) What was Mr. Zhang's monthly wage and salary income in January 2006?
(2) Were Mr. Liu's and Mr. Wang's monthly wage and salary incomes the same in January 2006?
Let's assume that Mr. A's total monthly salary and wage income in January 2006 is $x$ yuan, the tax due is $y_{1}$ yuan, the tax due in the past is $y_{2}$ yuan, and the underpaid tax is $y$ yuan, then $y=y_{2}-y_{1}$.
When $0 \leqslant x \leqslant 1600$, $y_{1}=0$.
When $1600<x \leqslant 2100$, $y_{1}=5 \% \cdot(x-1600)=0.05 x-80$.
When $2100<x \leqslant 3000$, $y_{1}=500 \times 5 \%+10 \% \cdot(x-2100)=0.1 x-185$.
When $0 \leqslant x \leqslant 800$, $y_{2}=0$.
When $800<x \leqslant 1300$, $y_{2}=5 \% \cdot(x-800)=0.05 x-40$.
When $1300<x \leqslant 2800$, $y_{2}=5 \% \times 500+10 \% \cdot(x-1300)=0.1 x-105$.
When $2800<x \leqslant 3000$, $y_{2}=500 \times 5 \%+1500 \times 10 \%+15 \% \cdot(x-2800)$ $=0.15 x-245$.
When $0 \leqslant x \leqslant 800$, $y=y_{2}-y_{1}=0$.
When $800<x \leqslant 1300$, $y=y_{2}-y_{1}=0.05 x-40$. Then $0<y \leqslant 25$.
When $1300<x \leqslant 1600$, $y=y_{2}-y_{1}=0.1 x-105$. Then $25<y \leqslant 55$.
When $y=54$, $x=1590$.
Therefore, Mr. Zhang's total monthly salary and wage income in January 2006 is 1590 yuan.
When $1600<x \leqslant 2100$, $y=y_{2}-y_{1}=(0.1 x-105)-(0.05 x-80)=0.05 x-25$.
Then $55<y \leqslant 80$.
When $y=80$, $x=2100$.
Therefore, Mr. Liu and Mr. Wang's total monthly salary and wage income in January 2006 can be 2100 yuan.
When $2100<x \leqslant 2800$,
$$
y=y_{2}-y_{1}=(0.1 x-105)-(0.1 x-185)=80 \text{. }
$$

Therefore, Mr. Liu and Mr. Wang's total monthly salary and wage income in January 2006 can be more than 2100 yuan and not exceed 2800 yuan.
When $2800<x \leqslant 3000$,
$$
\begin{array}{l}
y=y_{2}-y_{1}=(0.15 x-245)-(0.1 x-185) \\
=0.05 x-60 .
\end{array}
$$

Then $80<y \leqslant 90$.
In summary, Mr. Zhang's total monthly salary and wage income in January 2006 is 1590 yuan, and Mr. Liu and Mr. Wang's total monthly salary and wage income is no less than 2100 yuan and does not exceed 2800 yuan. Therefore, Mr. Liu and Mr. Wang's total monthly salary and wage income in January 2006 can be different.