Question 663702
Let x = the number of original business owners

$1000 / x = the amount each business owner paid

When 5 business owners were lost, there were x - 5 left and they had to pay what the 5 business owners would not. The 5 business owners paid

5 * ($1000 / x)

so we now pay this with $10 each from the remaining business owners

5 * ($1000 / x) = $10 * (x - 5)

Doing some algebra, we get

5 * 1000 / x = 10 (x - 5)

5000 = 10 * x * (x - 5)
500 = x^2 - 5x
x^2 - 5x - 500 = 0
(x - 25) * (x + 20) = 0
x = 25 OR x = -20

x can only be positive so x must be 25.

Checking the answer, we get 25 original business owners paying $1000 / 25, or $40 each. When 5 fold, there are 20 left and they have to pay the difference. Five business owners would have paid 5 * $40 which equals $200. The 20 remaining business owners pay $10 each so $10 * 20 equals to $200, so this is correct.

Therefore, there were 25 business owners in the original group.