To calculate the VAT element of a price which already includes 15% VAT, use one of these methods:
Method 1: Multiply by 15 and divide by 115. (That's exact)
Method 2: Multiply by 0.13043. That's not exact but it's given to 5 significant figures, so it's good enough unless you're working with exceptionally large sums of money. Your (incorrectly stated) multiplier for 17.5% used a similar degree of accuracy.
Method 3: Calculate the non-VAT price by dividing by 1.15, and then subtract that from the VAT inclusive price. (That's an exact method).
Chris