2. 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 $25 \%$, what would be the new selling price of the sweater?
(A) $62.50 €$
(B) $64.00 €$
(C) $62.83 €$
(D) $62.10 €$
(E) $62.00 €$
(2) The correct answer is $(A)$.

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 $25\%$ VAT is therefore $p^{\prime \prime}=p+\frac{25}{100} p=\frac{125}{100} p=\frac{125}{100} \cdot \frac{100}{122} p^{\prime}=\frac{125}{122} p^{\prime}$. Given that $p^{\prime}=61 €$, it follows that $p^{\prime \prime}=62.50 €$. Question proposed by Carmelo Di Stefano.