60. How much land was there?

- We'll see if you are good at practical arithmetic,- said the Black Queen. - A small farmer had no money to pay taxes. To settle the debt, the royal tax collector cut off one tenth of the land owned by the farmer, after which the farmer was left with ten acres of land.

How much land did he have at first?

Alice was about to give the wrong answer, but
she promptly caught herself, thought for a moment, and found the right answer.

How much land did the farmer have?
60. How much land is there? The problem usually gives an incorrect answer: 11 acres. If the farmer originally owned 11 acres of land, the tax collector would have cut off $1 \frac{1}{10}$ acres (which is $1 / 10$ of 11 acres), and the farmer would be left with $99 / 10$ acres instead of 10, as required by the problem. Therefore, 11 acres cannot be the correct answer.

How to get the correct answer? Let's approach the solution as follows. After the tax collector cut off $1 / 10$ of the plot, the farmer was left with $9 / 10$ of the original plot area. Thus, $9 / 10$ of the original plot area equals 10 acres. This means that multiplying the original plot area by $9 / 10$ gives the area of the reduced plot, which is 10 acres. Therefore, to return from the area of the reduced plot to the area of the original plot, the area of the reduced plot must be divided by $9 / 10$! As is known, dividing by $9 / 10$ is the same as multiplying by $10 / 9$, so multiplying 10 acres by ${ }^{10} / 9$ gives ${ }^{100} / 9$, or $11^{1} / 9$ acres.

Verification. The area of the original plot is $11 \frac{1}{9}$ acres. One tenth of $11 \frac{1}{9}$ is $1 \frac{1}{9}$. After cutting off $1 \frac{1}{9}$ acres, a plot of exactly 10 acres remains.