The ratio of the earnings of A, B and C is 2 : 3 : 5. If A increases his earnings by a certain amount, B by double that amount and C by triple that amount, which of the following could be the ratio of the earnings of A and C after the increase?
Question
The ratio of the earnings of A, B and C is 2 : 3 : 5. If A increases his earnings by a certain amount, B by double that amount and C by triple that amount, which of the following could be the ratio of the earnings of A and C after the increase?
Solution
The problem doesn't specify the amount by which A increases his earnings, so let's assume that amount to be x.
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Initially, the earnings of A, B, and C are 2k, 3k, and 5k respectively (where k is a constant).
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After the increase, A's earnings become 2k + x, B's earnings become 3k + 2x, and C's earnings become 5k + 3x.
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The new ratio of A's earnings to C's earnings is (2k + x) : (5k + 3x).
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To simplify this ratio, we can divide both parts by k (assuming k ≠ 0). This gives us a ratio of (2 + x/k) : (5 + 3x/k).
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Since we don't know the value of x or k, we can't simplify this ratio any further. However, we can see that the ratio of A's earnings to C's earnings will increase if x/k is greater than 0, and decrease if x/k is less than 0.
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Therefore, any ratio that is greater than the initial ratio of 2 : 5 could potentially be the ratio of the earnings of A and C after the increase.
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