Answer
$20$ people
Work Step by Step
Step 1. Assume there are originally $x$ number of people in the group; then the original average price is $\frac{600000}{x}$
Step 2. Adding 5 more, we have $x+5$ people and the new average price is $\frac{600000}{x+5}$
Step 3. Based on the given condition, we have $\frac{600000}{x}-\frac{600000}{x+5}=6000$ or $\frac{100}{x}-\frac{100}{x+5}=1$
Step 4. Multiply $x(x+5)$ on both sides; we have $100x+500-100x=x(x+5)$ or $x^2+5x--500=0$
Step 5. Factor the above equation to get $(x+25)(x-20)=0$; discarding the negative solution, we get $x=20$
