# The most difficult problems

#### Number of problems found: 5766

- Car repair

John bought a car for a certain sum of money. He spent 10% of the cost to repairs and sold the car for a profit of Rs. 11000. How much did he spend on repairs if he made a profit of 20%? - Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Ratio of sides

Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7. - A photograph

A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm^{2}. Find the size of paper and photo. - 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? - Castle model

The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm^{2}of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of woo - The difference

The difference of two numbers is 1375. If their exact quotient is 12. Find the two numbers - Profit growth

The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods? - Athletic competition

In a 400 meter athletic competition, a participant covers the distance as given below. find the average speed? first 80 meters 10 m/s next 240 meters 7.5 m/s last 80 meters 10 m/s - Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand. - A screen

A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size? - Mixing Celsius and Fahrenheit

Add up three temperatures: 5°F +6°F +0°C - Hyperbola equation

Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Coordinates of square vertices

The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square. - Closed drum

Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm . (π= 3.14) - KLM triangle

Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees. - Find the sum

Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5 - The size

The size of a Trapezium are 3/4×cm, ×cm 2(×+1)cm and 3(×+2)cm long respectively if it's perimeter is 60cm, calculate the length of each side. - Sum of dividend

If X is divided separately 2.63 and 1.40. And the results of the individual divisions are added to give a result less than X. What is X? - Unknown mixed number

Find the number that is smaller than 5 5/12 by as much as 2 2/13 is smaller than 6 1/6

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