Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 397. (December 2013)

K. 397. A certain island that is also a country has its own currency, the wooden knut. Everyone pays tax to the state (independently of the size of his or her income). The tax is a certain percentage of the income. However, the government supports the raising of children, therefore every family receives a tax reduction of a certain number of wooden knuts per child (for example, the reduction is twice as many wooden knuts for two children as for a single child). One particular family has an annual income of 1500000 wooden knuts and one child. They pay a tax of 150000 wooden knuts. Another family has an annual income of 2500000 wooden knuts, two children and a tax of 225000 wooden knuts to pay. What percentage of the income is the tax on the island, and what is the tax allowance per child?

(6 pont)

Deadline expired on January 10, 2014.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Az egy gyerekes család legyen a Kis család, a kétgyerekes pedig a Nagy család. Kisék családját „duplázzuk” meg. Eszerint, ha valakinek 3 000 000 fabatka a jövedelme és két gyereke van, akkor 300 000 fabatka a befizetendő adója. Ez azt jelenti, hogy Nagyék családjához képest a jövedelem 500 000 fabatkával több, és az adó pedig 75 000 fabatkával nagyobb. Tehát 500 000 fabatka után gyerek nélkül a befizetendő adó 75 000 fabatka, vagyis 15%. Kiséknek tehát gyerek nélkül 225 000 fabatka adót kéne fizetniük, így egy gyerek után 75 000 fabatka adókedvezmény jár.

### Statistics:

 198 students sent a solution. 6 points: 94 students. 5 points: 17 students. 4 points: 9 students. 3 points: 5 students. 2 points: 6 students. 1 point: 13 students. 0 point: 38 students. Unfair, not evaluated: 16 solutionss.

Problems in Mathematics of KöMaL, December 2013