Problem 3. In the park, there were lindens and maples. Maples among them were $60 \%$. In spring, lindens were planted in the park, after which maples became $20 \%$. In autumn, maples were planted, and maples became $60 \%$ again. By what factor did the number of trees in the park increase over the year?

[6 points] (D.E. Shnol)
Answer: 6 times.

First solution. Before the planting, lindens constituted $2 / 5$, and maples $-3 / 5$ of all the trees in the park. By summer, the number of maples did not change, but they began to constitute $1 / 5$ of all the trees. Therefore, the total number of trees in the park increased threefold. At the same time, lindens constituted $4 / 5$ of all the trees.

By winter, the number of lindens did not change, but they began to constitute $2 / 5$ of all the trees. Therefore, the total number of trees increased by another factor of two. Thus, over the year, the number of trees increased by a factor of 6.

Second solution. At first, there were 1.5 times fewer lindens than maples, and then there were 4 times more. While the number of maples did not change. Therefore, the number of lindens increased by $1.5 \cdot 4 = 6$ times. Note that by the end of the year, the ratio of the number of maples to the number of lindens became the same as it was at the beginning.

Since the number of lindens did not change in the fall, the number of maples also increased by six times. That is, the number of trees in the park increased by six times.