If I have a figure to which I have to apply an additional 17.5% say $100
so
that it eqals $117.5. What formula do I use to work out what the original
starting price was when I am confronted by $117.50 ie I want to get back
to
the $100 figure. So in this case 17.5% up is what formula to go down and
what is the rule for going down from an number.

If the original price is X and you want to get the price with 17.4% tacked
on, you multiply by 1.175. This comes from doing this...

X + 0.175 * X = 1.175 * X (factor out the common X term)

So, the formula to go up is New = (1 + PercentAsDecimal) *Old

Hence, to go the other way, divide the above by (1+PercentAsDecimal).
Thus...

Old = New / (1 + PercentAsDecimal)

Example, what was the original price if $117.50 represents a 17.5% markup...

Old = $117.50 / 1.175 = $100

Rick