# Ratio + reason - math problems

On solving problems and tasks with proportionally, we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members make possible to calculate the fourth - unknown member.

1. 1st drug First drug pack has an active ingredient ratio of L1: L2 = 2: 1 Second drug pack have a ratio of active ingredients L1: L2 = 1: 3 In which ratio do we have to mix the two packages so that the ratio of substances L1: L2 = 1: 2?
2. Two rectangles 2 A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
3. Painters Ten painters paint the school in 20 days. How many days do four painters paint the school at the same pace of work?
4. Barter There is exchange trade on the market. We know that for two sheepskins we get three goat skins. We also know that for six rabbits skins we get four goat skins. How many rabbit's skins we get for four sheepskins?
5. The work The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take?
6. Collection of stamps Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
7. 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?
8. 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.
9. Apples School kitchen bought 36kg apples for 12 kc/kg. How many kilograms of apples 1/4 cheaper can they buy for the same money?
10. Gold inheritance The king divided the inheritance with his three sons in the ratio of 7: 6: 4. Two of them received 286,000 gold. How much each of the sons got.
11. Three friends Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
12. Oranges Mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there?
13. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
14. Ratio of two unknown numbers Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
15. Three numbers The sum of the three numbers is 287. These numbers are in a ratio of 3: 7: 1/4 Define these numbers
16. Baker The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough?
17. Cuboid and ratio Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
18. Flowerbed Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of th
19. Candelas We burned two unequally thick and long candles. Longer burnt for three and a half hours and shorter for five hours. After two hours of burning it was identical. How many times was longer candle longer then shorter?
20. Cows 20 cows has food for 60 days. We reduce the dose to two-thirds for 18 cows. How many days will be fed?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Check out our ratio calculator.