1. The head of a fish weighs as much as the tail and half of the body, the body weighs as much as the head and tail together. Its tail weighs 1 kg. How much does the fish weigh?

2. The student had to divide the number by 2 and add 3 to the result, but he, by mistake, multiplied the number by 2 and subtracted 3 from the resulting quotient. The answer was still correct. Which?

3. One sapphire and two topaz are three times more valuable than an emerald. And seven sapphires and topaz are eight times more valuable. I ask you to determine whether sapphire is more valuable or topaz?

4. Four friends are buying a boat. The first one contributes half the amount contributed by the others; the second - a third of the amount contributed by the others; the third - a quarter of the amount contributed by the others; fourth - 130 rubles. How much does the boat cost?

5. Michael bought a batch of pens at the wholesale market and offers customers either one pen for 5 rubles, or three pens for 10 rubles. Michael receives the same profit from each buyer. What is the wholesale price of the pen?

6. Think of 45 as the sum of four numbers so that after adding 2 to the first number, subtracting 2 from the second number, multiplying the third number by 2, and dividing the fourth number by 2, the numbers become equal.

7. The tourist went 20 km up the river in a boat and came back down, spending 10 hours doing it all. The journey against the current took one and a half times longer than the return journey. Find the speed of the river flow.

8. The team of mowers had to mow two meadows, one of which was twice the size of the other. For half a day the team mowed a large meadow, and for the second half of the day it was divided in half. One half remained to finish mowing the large meadow, while the other began to work on the small one. By evening, the large meadow was mowed, but what remained of the small one was a section that was mowed the next day with one mow. How many mowers are there in the artel?

9. Two cyclists left at the same time from the same point in the same direction. The first of them travels at a speed of 15 km/h, the second at a speed of 12 km/h. Half an hour later, a third cyclist left the same point, who after some time caught up with the second, and after another hour and a half, caught up with the first. Find the speed of the third cyclist.

10. From a hot tap, the bathtub fills in 23 minutes, from a cold tap - in 17 minutes. Pierre opened the hot tap first. After how many minutes should he open the cold one so that by the time the bath is filled, the hot water will be 1.5 times more than cold?

11. A tourist walking from a village to a railway station, having walked 3 kilometers in the first hour, calculated that he would be 40 minutes late for the train. Therefore, he walked the rest of the way at a speed of 4 km/h and arrived at the station 45 minutes before the train departed. What is the distance from the village to the station?

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