B4. Three pipes sometimes fill a pool. The first pipe can fill the pool on its own in four hours, the second in ten hours, and the third in twenty hours. What percentage of the pool is filled if all three pipes are opened for two hours? Write your answer.

## PROBLEMS FOR THE SECOND YEAR

Before you are two sets of problems. Problems 1 to 6 of the first set are solved by selecting the correct answer from the five proposed answers on this sheet and writing it in the table under the corresponding number. Only one answer is correct. A correct answer will be scored with two points, while a wrong answer will result in the deduction of one point.

Problems 1 to 4 of the second set are solved on the provided paper. The solution to each of these problems will be evaluated on a scale from 0 to 6 points. On the sheets where you will solve the problems, do not sign, but write only your code. Write your solution clearly and legibly with a pen.

The time for solving is 90 minutes.

THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-04.jpg?height=174&width=488&top_left_y=895&top_left_x=801)

## PART I
B4. If the first pipe fills $\frac{1}{4}$ of the pool, the second $\frac{1}{10}$, and the third $\frac{1}{20}$, then if all three pipes are opened for two hours, they will fill $\frac{1}{2}+\frac{1}{5}+\frac{1}{10}=\frac{8}{10}$ of the pool, which is $80\%$.

Correct expression for all three pipes in one hour ..............................................................................................

Correct expression for all three pipes in two hours ..........................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-11.jpg?height=68&width=1642&top_left_y=1077&top_left_x=273)

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-11.jpg?height=71&width=1639&top_left_y=1135&top_left_x=274)

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-11.jpg?height=54&width=1639&top_left_y=1184&top_left_x=274)

Written answer . .............................................................................................

## Second Year

I. PART

| Task | A1 | A2 | A3 | A4 | A5 | A6 |
| :--- | ---: | ---: | ---: | ---: | ---: | :---: |
| Answer | B | D | C | A | E | B |