1. Each of the 5 brothers owns a plot of land. One day, they pooled their money, bought a neighbor's garden, and divided the new land equally among themselves. As a result, Andrey's plot increased by $10 \%$, Boris's plot - by $\frac{1}{15}$, Vladimir's plot - by $5 \%$, Grigory's plot - by $4 \%$, and Dmitry's plot - by $\frac{1}{30}$. By what percentage did the total area of their land increase as a result?
Answer: By $5 \%$.

Solution. Let A, B, V, G, D be the areas of the plots of each brother, respectively. Then, according to the problem, $\frac{1}{10} \mathrm{~A}=\frac{1}{15} \mathrm{~B}=\frac{1}{20} \mathrm{~V}=\frac{1}{25} \mathrm{~G}=\frac{1}{30} \mathrm{~D}$ (*). Denoting $\mathrm{A}=x$, we find: $\mathrm{B}=1.5 x, \mathrm{~V}=2 x, \mathrm{~G}=2.5 x$, D $=3 x$. Therefore, the total area of their plots was $10 x$, and increased by $\frac{1}{10} \mathrm{~A}=0.1 x$ for each, that is, by $0.5 x$ in total. Thus, the increase amounted to $\frac{0.5 x}{10 x} \cdot 100 \% = 5 \%$.

Comment. The relationship (*) is obtained - 2 points. The correct answer is obtained in the case of a particular example - 2 points. If arithmetic errors are made in the correct solution process, deduct $1-2$ points.