# Examples for 9th grade - page 3

1. Clogging
How much distilled water must the pharmacist add to 30g of a 30% hydrogen peroxide solution to obtain a 3% solution to clogging?
2. Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
3. Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
4. Three friends
Cuba, Matthew and their friend Adam found a brigade during their weekend weekends because they wanted to make a joint trip to the Alps that they planned for the spring break. Cuba enjoyed the skiing trip very much, so he was not lazy to get up and went t
5. Vinegar mixing
We mix 70g water and 50g 8% vinegar. How many percents of the solution of vinegar we produce?
6. Two trains
Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak
7. Mushrooms
Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
8. Waste
How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
9. Three machines
The power of the three machines is 2: 3: 5. Two most powerful machines produce 400 parts per hour. How many components make all three machines in 3 hours?
10. Helmet
In nowadays cycling better results could be obtained not only due to rider physical preparation but also thanks to using updated technologies. One of the most important part of rider´s equipment is his or her helmet. While most bikers wear a helmet mainly
11. Tractors
Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor?
12. Chocolate
I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate.
13. Ages 2
A man's age is 4 times his son's age. After 5 years he will be just twice his son's age, find their ages.
14. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
15. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
16. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
17. Bonus
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
18. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
19. Troops
Route is long 147 km and the first day first regiment went at an average speed 12 km/h and journey back 21 km/h. The second day went second regiment same route at an average speed 22 km/h there and back. Which regiment will take route longer?
20. Logic
A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together?

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