# Martin Management

**Algebra**Level 5

\(\color{Green}{Marloutte}\) is a clever trader , very smart and intelligent. Once, he ordered some apples for trading. The contractor sent his merchant to deliver the apples.

The contractor lived in \(\color{Blue}{Mersaills}\), while \(\color{Green}{Marloutte}\) lived in \(\color {LimeGreen}{Mosaques}\). The distance between two cities was 9000 kilometres.

The name of the merchant was \(\color{Red}{Martin}\). His horse, \(\color{Purple}{Mineraques}\), could carry a maximum of \(q\) apples at a time. \(\color{Red}{Martin}\) was a greedy man, when he was transporting the apples, he ate one apple for one kilometer. But being equally shrewd, he in that way carried the maximum number of apples as he could using some technique.

When he reached \(\color {LimeGreen}{Mosaques}\) , he gave the remaining apples to \(\color{Green}{Marloutte}\). \(\color{Green}{Marloutte}\) knew that \(\color{Red}{Martin}\) had eaten some apples as it was obvious. On asking, \(\color{Red}{Martin}\) told him that for every kilometre he travelled he used to eat an apple as he was so greedy that on seeing the apples he could not control himself. He told \(\color{Green}{Marloutte}\) that the total number of the apples he carried from Mersaills was \(5q\), and he now is left with only 690 apples.

\(\color{Green}{Marloutte}\) soon figured out how much apples he began with such that the maximum number of apples he is left with is 690. Can you figure out how many apples \(\color{Red}{Martin}\) began with such that if he eats one apple for every kilometer he travels then the maximum number of apples he could transfer is 690?

ASSUMPTIONS :\(\color{Red}{Martin}\) could never control his greed means for every one kilometre he has to and definitely has to eat one apple. Based on his this habit he devised a way to transfer the maximum number of apples he could.

The horse could travel as much as you want it to.

Well, you may as well assume the minimum distance the horse can travel is one kilometer, meaning that one kilometer is the unit in which you will solve the problem , no meters or anything else. This is for the sake of clarity so that the question reamins logical , realistic and does not go into abstract maths or calculus.

And finally assume everything is in integers, of course positive , that he ate a integer number of bananas each time etc. \(\color {Pink}{REMEMBER}\) It is a big hint to the question and may be the key to it.

And of course this problem is a converse of another problem that I liked which shall be revealed in the solution.

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