Problem K. 785. (November 2023)

K. 785. In the shops of three merchants Ali, Selim and Khafim a barrel of olives had the same price at the beginning of June. Ali increased the price by 10%, then by 10% again, and then at the beginning of September decreased the price by 20%. Selim increased the price by 20%, then decreased it by 10%, and then at the beginning of September decreased it by 10% again. Khafim increased the price by 20%, and then at the beginning of September decreased it by 20%. We know that at the beginning of September Ali sold a barrel of Olives 4 dinars cheaper than Selim. How much did a barrel of olives cost at the beginning of September in Khafim's shop?

(5 pont)

Deadline expired on December 11, 2023.

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

Megoldás. Legyen egy hordó olajbogyó júniusi ára \(\displaystyle x\) dénár. Ali az árrendezések után \(\displaystyle x\cdot 1,1\cdot1,1\cdot0,8 = 0,968x\) dénárért adott egy hordóval. Szelim szeptember elején \(\displaystyle x\cdot1,2\cdot0,9\cdot0,9 = 0,972x\) dénárért adott egy hordót. A két ár között a különbség \(\displaystyle 0,004x\), ez \(\displaystyle 4\) dénár, tehát \(\displaystyle 1\) hordó olajbogyó ára június elején \(\displaystyle 1000\) dénár volt. Így Kháfim szeptember elején \(\displaystyle 1000\cdot1,2\cdot0,8 = 960\) dénárért adott egy hordó olajbogyót.

Statistics:

135 students sent a solution.
5 points:	52 students.
4 points:	11 students.
3 points:	7 students.
2 points:	2 students.
1 point:	2 students.
Unfair, not evaluated:	1 solutions.
Not shown because of missing birth date or parental permission:	60 solutions.

Problems in Mathematics of KöMaL, November 2023