Gemara

37a (Mishnah): If Reuven told two people 'I stole from one of you, and I don't know from which', or 'one of your fathers deposited money with me, but I don't know which', he pays both, because he admitted by himself.

If one person deposited 100 Zuz with Reuven, and another person deposited 200, and each claims that he gave 200, and Reuven does not know who gave which, he gives each 100. We leave the rest until Eliyahu comes;

R. Yosi says '(this is improper,) for if so, the swindler does not lose (he has no incentive to admit)! Rather, all the money is left until Eliyahu comes.

Similarly, if they deposited Kelim, and each claims the bigger Kli, one gets the smaller Kli, we give the other the value of the smaller from the larger, and we leave the rest;

R. Yosi says, we leave all of it.

Inference: The Reisha teaches that when in doubt, we make someone pay. We do not say 'to take money from another, one must bring proof';

Contradiction: In the Seifa, Reuven does not pay due to his doubt!

Answer: If one stole, Chachamim fined him to pay out of doubt. They did not fine one who accepted deposits.

Contradiction: In our Mishnah, a thief is fined. In another Mishnah, he leaves in front of them what he stole, and walks away!

Answer: In that Mishnah, they claim from him. Letter of the law, he leaves in front of them what he stole, and walks away. In our Mishnah, Reuven wants to fulfill his obligation b'Yedei Shamayim, so he pays each.

The Mishnah needed to teach about deposits or money and Kelim:

Had it taught only about money, one might have thought that there Chachamim say to return 100 to each, for there is no loss, but regarding Kelim, there is a loss, and Chachamim would admit to R. Yosi;

Had it taught only about Kelim, one might have thought that there R. Yosi says that we leave them until Eliyahu comes, but regarding money, since we can give each 100 without a loss, he admits to Chachamim.

Objection: R. Yosi's reason is in order that the swindler will admit! (Surely he argues even when there is no loss!)

Retraction: Rather, both cases come to taught to teach Chachamim's opinion. The case of Kelim is a bigger Chidush than the case of money.

Rishonim

Rif: The Shomer must pay, for he was negligent for not writing how much each gave, lest he forget.

Rambam (Hilchos She'elah 5:4): If one person deposited 100 Zuz with Reuven, and another person deposited 200, and each claims that he gave 200, and Reuven does not know who gave which, each swears, like one who swears and receives, that he gave 200. Reuven pays 200 to each, and loses 100 from his money. He was negligent; he should have written the name of each depositor on his bag.

Magid Mishneh: Even though Reuven admits that he owes 100 to each and is unsure about the rest, this is unlike one who admits to half a claim and is unsure about the rest. There, (since he cannot swear,) he pays without any oaths. Here, he knows that he received only 300, and due to his negligence he pays extra improperly. Therefore, it is proper that those who take must swear. The Rashba says so. Also, this law is even if he says Heilach (and gives the 100 to each that he admits to), and then Modeh b'Miktzas does not apply.

Rambam (ibid): Similarly, if they deposited Kelim, and each claims the bigger Kli, they both swear, and he gives the big Kli to one, its value to the other, and keeps the small one. If they deposited together one bundle, he gives the smaller Kli to one, its value to the other from the big Kli, and holds the rest until one of them admits, or forever. Similar, if two claim a deposit, and Reuven says 'it was from one of you; I do not know which', he pays both of them.

Rosh (3:8): The Reisha discusses when their fathers deposited. If they themselves deposited, Reuven would be exempt even b'Yedei Shamayim, for they would be negligent for forgetting. If one of two deposited and does not claim, Reuven is exempt even b'Yedei Shamayim, for the depositor should have been careful to remember. If two claim a deposit, and Reuven says 'it was one of you; I do not know which', each of them swears and collects. If they do not claim from him, he is exempt even b'Yedei Shamayim, for the depositor should have been careful.

Poskim

Shulchan Aruch (CM 300:1): If one person deposited 100 Zuz with Reuven, and another person deposited 200, and each claims that he gave 200, and Reuven does not know who gave which, each swears that he gave 200. Reuven pays 200 to each, and loses 100 from his money. He was negligent; he should have written the name of each depositor on his bag.

SMA (1): Each takes a severe oath, like one who swears and receives (82:2).

Gra (1): This is like a grocer who ordered to pay workers (and they argue about whether or not he paid them), or two lenders. They would collect without swearing if there were no dispute.

Shulchan Aruch (ibid): If they do not make Vadai claims from him, to be Yotzei Yedei Shamayim he is liable. He is exempt b'Yedei Adam.

SMA (3): He can say 'I was careful to see who gave 200, and I forgot.' They themselves forgot, for they did not claim from him!

Shach (5): If they do not claim at all, the last 100 is split among the depositors, for there is no liar.

Shulchan Aruch (2): Similarly, if they deposited Kelim, and each claims the bigger Kli, they both swear, and he gives the big Kli to one, its value to the other, and keeps the small one. If they deposited together one bundle, he gives the smaller Kli to one, its value to the other, and the rest is left until one of them admits, or forever.

SMA (10): The Gemara said that one might have thought that regarding Kelim we do not cause a loss, and Chachamim would admit to R. Yosi. The extra clause teaches that this is not so. The Tur omitted this, for it is obvious.

Gra (9): This is like the Rambam (we sell the larger Kli - Lechem Mishneh), unlike Rashi (37a DH Mitoch, who says that we break a piece off the larger Kli). According to the Rambam, this is called a loss because a person prefers his own things.

Shulchan Aruch (3): Similar, if two claim a deposit, and Reuven says 'it was one of you; I do not know which', he pays both of them.

SMA (11): He pays them after they swear. When one does not remember from whom he bought, he pays only once (222:2). The Nimukei Yosef explains that this is because a buyer normally pays immediately, and he was not obligated to be careful. A Shomer often guards for a long time; he should have been careful.

Taz: Tosfos (37a DH Hasam) asked from a Chasid who bought from one of two. He holds that that one who buys must be careful, unlike the Nimukei Yosef.

Rema: If they do not claim from him, he is exempt, even to be Yotzei Yedei Shamayim. If he says 'one of your fathers deposited with me; I do not know which', he pays both of them to be Yotzei Yedei Shamayim.

SMA (12): Since there was only one depositor, he can say that he expected only the depositer to claim it, so he did not need to be careful. This is why he must pay when one of their fathers deposited. The Shomer was negligent.

Shulchan Aruch (76:3): If Reuven says to two 'one of you lent to me. I do not know which', and they do not claim from him, he is exempt even b'Yedei Shamayim. Some say that he must pay both be Yotzei Yedei Shamayim.

SMA (5): Since they do not claim from him, this shows that the lender was not careful. Since the borrower saw this, he himself was not careful.

Shach (16): Piplulei Charifta (8:8) says that here he was not negligent, for he did not expect the lender to forget.

Shach (18): In Siman 300, the Rema: brought only the first opinion. Why didn't he comment here that it is primary? Surely we cannot distinguish a deposit from a loan! Sefer ha'Terumos (39:3:1) equates them. Also the Tur here learns from what the Rosh said about a deposit!

Gra (4): The first opinion holds that the Mishnah mentions a father, for had the depositor himself forgotten, the Shomer would be exempt even b'Yedei Shamayim. The latter opinion holds that it merely gives a common case. Normally, one does not forget what he deposited.