# Fractions - high school - examples

- Sphere radius

The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change? - 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. - Bonus

Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses? - Logic

A man can drink a barrel of water for 26 days, woman for 48 days. How many days will a barrel last between them? - Beer

After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille? - Cube in a sphere

The cube is inscribed in a sphere with volume 6116 cm^{3}. Determine the length of the edges of a cube. - River

Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors? - Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Cyclist

Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane? - TV fail

The TV has after 10,000 hours average 25 failures. Determine the probability of TV failure after 200 hours of operation. - Scrap

From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product? - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC. - Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm^{2}and 198 cm^{2}. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Dices

We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2? - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC. - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - Price of state

Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 868 (super-gross wage).Then tax him 35.2% employer contributions

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