Two hens sold a total of 110 eggs at the market, and although one had more eggs than the other, they both had the same income. "If I had as many eggs as you did and sold them at the same price as my own," says one hen to the other, "I would have earned 5 K." "If I had sold your eggs at the same price as my own," replies the other, "my income would have been $7 \mathrm{~K} 20 \mathrm{f}$." How many eggs did each hen sell?
If one of the hens had $x$ eggs and both of them sold for $y K$, then one piece was sold for $\frac{y}{x} K$, and the other for $\frac{y}{110-x} K$.

According to the problem,

$$
\begin{aligned}
& (110-x) \frac{y}{x}=5 \\
& x \frac{y}{110-x}=7.2
\end{aligned}
$$

Eliminating $y$:

$$
\left(\frac{110-x}{x}\right)^{2}=\frac{25}{36}
$$

or

$$
\frac{110-x}{x}=\frac{5}{6}
$$

from which

$$
x=60 \text {. }
$$

Therefore, one hen sold 60 eggs, and the other sold 50 eggs.