Draw a table showing the total number of deliveries made to each region and the percentage of total deliveries made to each region.

Sum all deliveries from each region:

The total number of deliveries is 860000.

Percentage for a region = $\frac{\text{Deliveries for region}}{\text{Total Deliveries}} \times 100\%$

• Gauteng: $\frac{240000}{860000} \times 100\% \approx 27.91\%$
• Western Cape: $\frac{170000}{860000} \times 100\% \approx 19.77\%$
• KwaZulu-Natal: $\frac{150000}{860000} \times 100\% \approx 17.44\%$
• Eastern Cape: $\frac{95000}{860000} \times 100$
• Free State: $\frac{60000}{860000} \times 100$
• Limpopo: $\frac{50000}{860000} \times 100$
• Mpumalanga: $\frac{40000}{860000} \times 100$
• North West: $\frac{30000}{860000} \times 100$
• Northern Cape: $\frac{25000}{860000} \times 100$

Here is the completed table:

Original deliveries for Gauteng = 240000.
Increase = $10\%$ of $240000 = 0.10 \times 240000 = 24000$.
New deliveries for Gauteng = $240000 + 24000 = 264000$.

Deliveries for other regions (excluding Gauteng) remain the same:
$170000 + 150000 + 95000 + 60000 + 50000 + 40000 + 30000 + 25000 = 620000$.
New total deliveries = New Gauteng deliveries + Sum of other regions' deliveries
New total deliveries = $264000 + 620000 = 884000$.

New percentage for Gauteng = $\frac{\text{New Gauteng deliveries}}{\text{New Total Deliveries}} \times 100\%$

The new percentage of deliveries in Gauteng is \boxed{\text{29.86%}}.