A10. The price of a product is first reduced by $50 \%$, then the reduced price is further reduced by another $50 \%$. By what percentage would we need to reduce the price of the product at the beginning to make the final price of the product the same as after the second reduction?
(A) by $25 \%$
(B) by $66 \%$
(C) by $75 \%$
(D) by $100 \%$
(E) depending on the initial price of the product
A10 A product with a price of $a$ has a price of $0.5a$ after a $50\%$ discount. After an additional $50\%$ discount, the price of the product is $0.5a \cdot 0.5 = 0.25a$, which represents $25\%$ of the original price. The same price is obtained if a single discount of $75\%$ is applied.

A competitor can earn a maximum of 5 points for each problem. A competitor who arrives at the solution by any correct method (even if the scoring guide does not provide for it) receives all possible points.

A correct method takes into account each procedure that

- sensibly considers the wording of the problem,
- leads to the solution of the problem,
- is mathematically correct and complete.