14) $\mathrm{Al} 22$ November 2012, the price of gasoline is given 35% by the cost of the product, which is made up of various items (oil, refining, distribution costs, etc.); the cost of oil constitutes today 24% of the cost of the product. Knowing that on January 1, 2013, the price of oil will increase by 10% and other costs will remain unchanged, by how much will the price of gasoline increase on that date?
(A) $10 \%$
(B) $2.4 \%$
(C) $3.5 \%$
(D) $0.84 \%$
(E) none of the above
14. The answer is $(\mathbf{D})$.

![](https://cdn.mathpix.com/cropped/2024_04_17_ed8bf509241053ca04f5g-4.jpg?height=488&width=556&top_left_y=1198&top_left_x=1446)

Let $B$ be the price of gasoline today, and let $P$ and $O$ be the cost of the product and the cost of oil, respectively, also referred to today. We know that

$$
P=\frac{35}{100} B \quad \text { and } \quad O=\frac{24}{100} P
$$

thus

$$
O=\frac{24 \cdot 35}{100 \cdot 100} B=\frac{8.4}{100} B .
$$

Consequently, today the cost of oil constitutes 8.4% of the price of gasoline. If the cost of oil increases by $10 \%$ (i.e., by a tenth) and all other costs remain unchanged, the price of gasoline will increase by a tenth of 8.4%, i.e., by 0.84%. [Problem proposed by C. Di Stefano.]