Arrange the number of people who commute to work (in '000s) and the private to public transport percentages.

Steps to Solve

1. Identify Total Commuters in Each Year
   The total number of commuters in Year 1 is 300,000 (150,000 using public transport and 150,000 using private transport).
   In Year 2, the total number of commuters can be calculated as follows:

   • Number of people commuting to work in Year 2 = Number in Year 1 + 5,000
     $$ 300,000 + 5,000 = 305,000 $$

2. Calculate Public Transport Commuters for Year 2
   We know that 41,400 used public transport in Year 2. Thus, the percentage can be calculated as follows:

   $$ \text{Percentage of public transport} = \frac{\text{Public transport commuters}}{\text{Total commuters in Year 2}} \times 100 $$
   $$ = \frac{41,400}{305,000} \times 100 \approx 13.57% $$

3. Calculate Private Transport Commuters for Year 2
   The remaining commuters used private transport. Thus, we calculate:

   • Private transport in Year 2
     $$ \text{Private transport} = \text{Total commuters} - \text{Public transport} $$
     $$ = 305,000 - 41,400 = 263,600 $$

   • The percentage can be calculated similarly:
     $$ \text{Percentage of private transport} = \frac{\text{Private transport commuters}}{\text{Total commuters in Year 2}} \times 100 $$
     $$ = \frac{263,600}{305,000} \times 100 \approx 86.43% $$

4. Simplify the Data for Both Years
   To summarize the results:

   • Year 1:

     • Private Transport: 150,000 (50%)
     • Public Transport: 150,000 (50%)

   • Year 2:

     • Private Transport: 263,600 (86.43%)
     • Public Transport: 41,400 (13.57%)