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Mohammad is a merchant working at the Rabat open-air market. As usual he met two wholesalers early in the morning: Farid gave him $30$ melons to be sold at the price of $1$ dirham for three melons. Ali Hamza also gave him $30$ melons, but these one were a little bit more costly: he will have to sell them at the price of $1$ dirham for two melons. Given the prices at the end of the day he should earn $25$ dirhams in total: $10$ for selling Farid's melons plus $15$ for selling Ali Hamza's.

On their road to the open-air market, Mohammad thinks: "If I sell the cheaper melons first, no one will buy the second ones. But if I sell the expensive melons first, when I switch the price the customers will think that the cheaper ones are rotten and no one will buy them". That's a big problem for Mohammad, but suddenly he has an idea: "I could sell groups of $5$ melons for $2$ dirhams each". So he does and in short time the happy customers buy all the melons.

Now Mohammad is counting the money: he had $60$ melons in total, thus he sold $60/5 = 12$ groups of $5$ melons each earning $2$ dirhams for each group. He have $2 \times 12 = 24$ dirhams in his pockets, but wait a minute... he should have $25$ if he sold the melons at the original prices.

What happened to the missing dirham? Isn't selling $3$ melons for $1$ dirham and $2$ melons for $1$ dirham the same as selling $5$ melons for $2$ dirhams altogether?

I know this puzzle is a little bit too simple but I think it is a funny one.

Source: translated from the Italian book "Problemi di logica per ragazze e ragazzi svegli" (an old edition no more available for sale).

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    $\begingroup$ I'm afraid this puzzle is a duplicate: Where has Jones lost 1 Rs? $\endgroup$ Commented Jul 28, 2020 at 15:42
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    $\begingroup$ I'm still going to give it an upvote because the premise of the story amused me. But pity it was duplicate. $\endgroup$
    – Dreopa
    Commented Jul 28, 2020 at 15:47
  • $\begingroup$ sure it is a dupe, sorry about that. I searched on this website before posting but I couldn't find any duplicate because the story is totally different. I'm going to read this meta post now, hope it will help. $\endgroup$
    – melfnt
    Commented Jul 28, 2020 at 16:35
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    $\begingroup$ @melfnt If it's any consolation, it took me a while to find it. Out of desperation I searched for apples, and that was just a lucky guess. $\endgroup$ Commented Jul 29, 2020 at 7:37
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    $\begingroup$ No need to apologize - sometimes duplicates are hard to find! And having duplicate versions of the same question can be valuable: if they're differently phrased, this will help future people looking for the puzzle. $\endgroup$
    – Deusovi
    Commented Jul 29, 2020 at 14:53

1 Answer 1

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However, he only had 30 of the cheaper melons, so he could only make 10 groups containing 3 of the cheaper. So 10 groups of (3, 2) uses 30 cheap, and 20 expensive, leaving two groups of (0,5). These 10 melons should have been sold for 5 d, but he ended up selling them for 4d, losing 1d on the transactions.

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