How do I add a percentage to a value then subtract it again to get the same number?

Question

I'm doing a budget for work where I have to add $15\%$ to a price. But then my client is going to subtract $15\%$ from the total but I need to make the original price back. I.e.

$$£100.00 + 15\% = £115.00$$ $$£115.00 - 15\% = £97.75$$

My problem lies in that my client is unaware of the original number ($£100.00$) and I need to get this back as this is profit.

Answer 1

The percentage depends on your reference from which you take the it.

If you want to offer later on a $15$% discount to the customer, and keeping your "target budget" as it is, you want to reach $100$ after removing $15$% from $X$.

Thus $X*(1-\dfrac{15}{100})=100$ or else $X=\dfrac{100*100}{85}=117.647...$

Answer 2

Multiply by 1.15 to mark up. Divide by 1.15 to deduct the mark up.