# Latest problems

1. Winch
The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
2. Sphere floating
Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
3. Delayed clock
Michael put a new battery into his watch at midnight. However, they are 5 seconds late each minute. How many hours does the watch show in 24 hours?
4. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
5. Banknotes
How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions.
6. Concentric circles
There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
7. Number of songs
Write an expression for the number of songs they need for this show. Evan and Peter have a radio show that has 2 parts. They need 4 fewer than 11 songs in the first part. In the second part, they need 5 fewer than 3 times the number of songs in the first p
8. Photo frame
A square shape photo with a side length of 20 cm is framed by a 4 cm wide bar. Find the external frame size of this photo (the frame is from all sides)
9. Curiosity factor
A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?.
10. Lathe
95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
11. Former price
The price of an article is cut by 10℅, to restore it to the former value, by what percent the new price must be increased?
12. Percent change
If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
13. Tourist
A tourist walked an average speed of 3.5 km/h route in 6 hours. Calculate how many hours he would have passed at an average speed of 5.5 km/h.
14. Diamond and diagonals
A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
15. Geometric plan
At what scale the building plan if one side of the building is 45m long and 12mm long on a plan?
16. Pupils
There are 27 pupils in the classroom. They can swim 21 and ski nine pupils. Neither swim nor ski three pupils. How many pupils can swim and ski?
17. Down syndrome
Down syndrome is one of the serious diseases caused by a gene mutation. Down syndrome occurs in approximately every 550-born child. Express the incidence of Down's syndrome in newborns at per mille.