54. Continuing her research with fractions, Tanya added 4 to the numerator of a certain fraction and 10 to the denominator. After simplifying, to her surprise, she got the original fraction. She tried the same with another fraction, but the result did not repeat. What fraction did Tanya originally have?
54. Let the original fraction be $\frac{a}{b}$, then $\frac{a+4}{b+10}=\frac{a}{b}$, from which $a b+4 b=$ $=a b+10 a, 2 b=5 a$ and $\frac{a}{b}=\frac{2}{5}$. Indeed $\frac{2+4}{5+10}=\frac{6}{15}=\frac{2}{5}$. For this case, such a fraction is unique.