Adriano, Bruno, César, and Daniel are four good friends. Daniel had no money, but the others did. Adriano gave Daniel one fifth of his money, Bruno gave one fourth of his money, and César gave one third of his money. Each gave Daniel the same amount. The amount Daniel now has represents what fraction of the total amount that his three friends initially had together?
(a) $\frac{1}{10}$
(b) $\frac{1}{4}$
(c) $\frac{1}{3}$
(d) $\frac{2}{5}$
(e) $\frac{1}{2}$
The correct option is (b).

Since each friend gave Daniel the same amount, let's say Daniel received $x$ reais from each of his three friends. Initially, then, Adriano had $5 x$ reais, Bruno had $4 x$ reais, and César had $3 x$ reais. It follows that the total initial amount of money the three friends had was $5 x+4 x+3 x=12 x$ reais. Since each of his three friends gave him $x$ reais, Daniel now has $3 x$ reais, which represents one fourth of the total of $12 x$. Therefore, he now has $1 / 4$ of the amount that his three friends initially had together.