Multiple choice

In the first alloy, Aluminium and Tin are in the ratio 1 : 2. In the second alloy the same elements are in the ratio 2 : 3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5 : 8, the ratio of these two alloys in the new alloy is

  1. 3 : 10

  2. 3 : 7

  3. 10 : 3

  4. 7 : 3
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A Correct answer
Explanation

Using the alligation rule: Alloy 1 (1/3 Al), Alloy 2 (2/5 Al), Target (5/13 Al). (2/5 - 5/13) : (5/13 - 1/3) = (26-25)/65 : (15-13)/39 = 1/65 : 2/39 = 3/195 : 10/195 = 3:10.

AI explanation

By the method of alligation on part-to-whole fractions, the fraction of Aluminium in the first alloy is 1/3 and in the second alloy is 2/5. The target fraction of Aluminium in the new alloy is 5/13. The ratio of the first alloy to the second alloy is the difference between the target and the second alloy's fraction to the difference between the first alloy's fraction and the target: (5/13 minus 2/5) to (1/3 minus 5/13). This evaluates to 1/65 to 2/39, which simplifies to 3 to 10. The ratio of the two alloys in the new alloy is 3 : 10.

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