Here if I understand Yash, his doubt is not about the plurality of the past tense verb won. After all, won can be both singular of plural in all the three persons.
His point is how three people can own a single bike, as if one owns the front wheel, the second the frame and third the back wheel. This is just amusing in the least. However, it is not uncommon to use a singular object for a general group; we often say most of the IT people have a house; most of the rural houses in Kerala have at least one Jack tree. The humans have a pair of eyes. This is a commonly accepted usage. Therefore, there is no need to bother much. A is good enough.
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