8. The selling price of an item is obtained by increasing the actual amount by a certain percentage, called VAT (a tax, which is then paid to the tax office). In a store, the selling price of a sweater is $61.00 €$, including VAT at $22 \%$. If the VAT were to increase to $24 \%$, what would the new selling price of the sweater be?
(A) $62.25 €$
(B) $62.22 €$
(C) $63.00 €$
(D) $62.00 €$
(E) $61.50 €$
(8) The correct answer is $(D)$.

Let $p$ be the actual price of the sweater (excluding VAT) and $p^{\prime}$ be the price including $22\%$ VAT, so $p^{\prime}=p+\frac{22}{100} p=\frac{122}{100} p$, which means $p=\frac{100}{122} p^{\prime}$. The price including $24\%$ VAT is therefore $p^{\prime \prime}=p+\frac{24}{100} p=\frac{124}{100} p=\frac{124}{100} \cdot \frac{100}{122} p^{\prime}=\frac{124}{122} p^{\prime}$. Given that $p^{\prime}=61 €$, it follows that $p^{\prime \prime}=62 €$. Question proposed by Carmelo Di Stefano.