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One of three events must happen: odds against the third from the odds of the other two

The same question, asked 2 times: 10 May 2023 S1*, 9 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S1

    142
    There are three events A, B, C, one of which must and only one can happen. The odds are 8:3 against A, 5:2 against B and the odds against C is 4317k\frac{43}{17k}, then value of k is

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  2. Question 2

    9 May 2024 S1

    132
    A, B, C are three events, one of which must and only one can happen. The odds in favor of A are 4:64:6, the odds against B are 7:37:3. Thus, odds against C are

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