If an item is worth x (dollars, pounds, euros, etc) then VAT is charged at a rate of r%.
The price, p, you pay for the item is x+rx/100=x(1+r/100).
In this question p=780 and r=15, so we can find x and therefore we can find the VAT component.
1.15x=780, x=780/1.15=678.26, the price before VAT is added.
15% of 678.26 must be 780-678.26=101.74 (rounding up);
or we can simply work out 15% of 678.26=0.15×678.26=101.74 approx. after rounding up.